Correcting and/or preventing errors during the measurement of coordinates of a work piece

ABSTRACT

An arrangement measures coordinates of a workpiece and/or machines the workpiece. The arrangement has a first part and a second part that can be moved relative to the first part. The relative mobility of the first and second parts is specified in addition to a possible mobility of a probe that is optionally additionally fixed to the arrangement. The mobility of the probe is specified by a deflection of the probe from a neutral position during a mechanical probing of the workpiece for the purpose of measuring the coordinates. A measuring body is arranged on the first or second part, and at least one sensor is arranged on the other part, i.e. on the second or first part. The sensor generates a measurement signal corresponding to a position of the measuring body and thus corresponding to the relative position of the first and second part.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation application of U.S. patent application Ser. No.14/131,605, filed Mar. 3, 2014; which was a national stage application,under 35 U.S.C. §371, of International application PCT/EP2011/061681,filed Jul. 8, 2011; the prior applications are herewith incorporated byreference in their entireties.

BACKGROUND OF THE INVENTION Field of the Invention

The invention relates to correcting and/or preventing errors during themeasurement of coordinates of a work piece. In particular, the inventionrelates to an arrangement for measuring coordinates of a work piece, amethod for producing such an arrangement and a method for operating suchan arrangement.

Coordinates of a work piece can be specified and measured in differentways. By way of example, the coordinates relate to a reference system,for example what is known as the laboratory system or the coordinatesystem relating to the work piece or a work piece holder. However, it isalso possible, for example, that dimensions of the work piece areregistered and specified, which dimensions relate to at least tworeference points of the work piece, e.g. a length, a width or adiameter. In order to determine the coordinates, coordinate measuringmachines (also abbreviated CMM in the following) or the users of thecoordinate measuring machines are dependent on knowing the position and,often, also the alignment of a probe for sensing the work piece, andalso the position and alignment of the work piece itself, or at leastknowing a possible change in the position and alignment. A change in theposition and alignment can occur, in particular, if work piece and probeare moved relative to one another in order to be able to undertakefurther measurements of the coordinates. Therefore, if different partsof an arrangement for measuring coordinates of a work piece are mobilerelative to one another, corresponding movements can lead to errors whenmeasuring the coordinates of the work piece. Examples of such relativemovements are rotational movements of a rotational device (this is thesubject matter of a first aspect of the present invention), movementswhen setting the position and/or alignment of a probe or probe head(which has a sensor system) for sensing the work piece for the purposesof determining the coordinates (this is the subject matter of a secondaspect of the present invention) and the mechanical bending due tomechanical forces and/or the thermal expansion or thermal contraction ofthe material of an arrangement for measuring coordinates or of a machinetool (this is the subject matter of a third aspect of the presentinvention).

All this mobility is given in addition to the movement of an optionallypresent probe, which movement the probe performs during the measurementof the coordinates of a work piece by mechanical sensing (i.e. while theprobe contacts the work piece). In particular, such probes which aredeflected from a neutral position during mechanical sensing of the workpiece due to the mechanical forces acting between work piece and probe,wherein the deflection is established and evaluated for the purposes ofdetermining the coordinates of the contact point, are known. Theadditional mobility therefore leads to errors when measuring thecoordinates.

SUMMARY OF THE INVENTION

It is an object of the present invention to specify an arrangement and amethod of the type mentioned at the outset, by means of which errorswhen measuring coordinates of a work piece can be corrected and/orprevented.

Proposed is an arrangement for measuring coordinates of a work pieceand/or for machining the work piece, wherein the arrangement has a firstpart and a second part, which has mobility relative to the first part,wherein the relative mobility between the parts is given in addition toa possible mobility of an optional probe additionally attached to thearrangement, which mobility is given during mechanical sensing of thework piece for the purposes of measuring the coordinates by a deflectionof the probe from a neutral position, wherein a measuring body isarranged on the first or second part and at least one sensor is arrangedon the other part, i.e. on the second or first part, wherein the sensoris configured to generate a measurement signal corresponding to aposition of the measuring body and hence corresponding to the relativeposition between the first and second part.

The at least one sensor and the at least one measuring body assigned tothe sensor are elements which are permanently present on thearrangement. In contrast to measurement systems which are arranged on anarrangement for the purposes of a single or repeated calibration,measured values can therefore be obtained during running operation ofthe arrangement, in particular during the operation of the coordinatemeasuring machine or the machine tool, and deviations from an idealand/or predetermined movement of the parts and/or an unwanted movementduring the operation of the arrangement can be established. It followsthat it is possible that the design of the arrangement is simplified andtherefore larger deviations from the ideal or predetermined movementoccur, or larger movements occur than is desired. Measuring thesemovements or deviations can be taken into account during operation, inparticular during the measurement of the coordinates of the work piece.One option for taking this into account lies in correcting the movementby calculation, in particular by means of a mathematical model. Themeasured values of the at least one sensor are preferably registered andtaken into account repeatedly.

In accordance with a corresponding method for producing such anarrangement, a first part of the arrangement and a second part of thearrangement are provided and the first and second part are configured tobe mobile relative to one another. Here, the relative motion of theparts is/will be made possible in addition to a possible mobility of anoptional probe additionally attached to the arrangement, which mobilityis given during mechanical sensing of the work piece for the purposes ofmeasuring the coordinates by a deflection of the probe from a neutralposition. A measuring body is arranged on the first or second part andat least one sensor is arranged on the other part, i.e. on the second orfirst part. The sensor is configured to generate a measurement signalduring the operation of the arrangement, which measurement signalcorresponds to a position of the measuring body and hence corresponds tothe relative position of the first and second part.

In accordance with a corresponding method for operating such anarrangement, a first part of the arrangement and a second part of thearrangement are moved relative to one another, wherein the relativemotion of the parts is made possible in addition to a possible mobilityof an optional probe additionally attached to the arrangement, whichmobility is given during mechanical sensing of the work piece for thepurposes of measuring the coordinates by a deflection of the probe froma neutral position. A measuring body is arranged on the first or secondpart and at least one sensor is arranged on the other part, i.e. on thesecond or first part, wherein the sensor is configured to generate ameasurement signal during the operation of the arrangement, whichmeasurement signal corresponds to a position of the measuring body andhence corresponds to the relative position of the first and second part.

In particular, the probe can be arranged on a measuring head or probehead, which enables the mobility of the probe and, in particular, alsoregisters the deflection by at least one sensor.

By way of example, the sensor can be a magnetoresistive sensor, a Hallsensor which operates in accordance with the electromagnetic HallEffect, an optical sensor, a sensor which operates in accordance withthe piezoelectric effect, a capacitive sensor, an Eddy current sensorembodied to measure the distance and/or relative position, or a sensorwhich operates in accordance with at least one of the aforementionedfunctionalities and/or in accordance with at least one functionalitywhich has not been mentioned. In particular, a multiplicity ofmagnetoresistive sensors and Hall sensors can also be arranged on acommon support, for example a micro-support similar to a microchip. Eachsensor on the common support then registers, in particular, a differentdegree of freedom of the movement. By way of example, using two suchsupports, which each carry three sensors for registering three linearlyindependent degrees of freedom and are arranged at different axialpositions, it is possible to register all degrees of freedom of themovement. As a result of the plurality of sensors on one support, it isalso possible to measure the direction of a magnetic field prevailing atthe location of the support. By way of example, optical sensors registerone of a plurality of markings, formed on the measuring body, when themarking is, from the view of the sensor, moving past. In a differenttype of optical sensors, e.g., a laser triangulation is performedand/or, like in the case of an interferometer, a comparison is performedwith a comparison light beam which is not influenced by the measuringbody. In a further type of optical sensors, patterns projected onto themeasuring body are registered.

The measuring body is, in particular, configured in accordance with themeasurement principle of the sensor. By way of example, the measuringbody can have a permanently magnetic material in order to be able tomeasure in accordance with the Hall Effect or the magnetoresistivemeasurement principle. Alternatively, or in addition thereto, themeasuring body (e.g. a cylinder or a spherical measuring body) can havean electrically conductive surface for a capacitive or inductive sensorand/or a mirroring surface for reflecting measurement radiation for anoptical sensor. A mirroring or partially reflecting surface can beformed on e.g. a cylindrical, spherical or toroidal measuring body. Inany case, the sensor generates a measurement signal, which containsinformation relating to the position of the measuring body and hencerelating to the relative position of the first and second part. In thecase of some measurement principles, such as e.g. in the case of agrating disk as measuring body, which carries a plurality of line-shapedmarkings in the style of a line grating, a single measurement signal ofthe sensor may not yet be sufficient to be able to evaluate informationrelating to the position or relative position. By way of example, ameter reading, which corresponds to the number of markings alreadyregistered in advance, and/or an initial position of the first andsecond part may additionally be required. If a plurality of at leastthree rotational position sensors are arranged distributed about therotational axis of a rotational device and if in each case a rotationalposition of the two parts of the rotational device which can be rotatedrelative to one another is registered by the individual rotationalposition sensors, the measurement signals supplied by the rotationalposition sensors can be used to establish and/or take into account atranslational movement (i.e. a movement of the two parts rotatablerelative to one another in a direction transverse to the rotationalaxis). This will be explained in more detail below. In the same case, orelse in the case of measurement systems with other sensors, acalibration of the sensor arrangement formed by the measuring body andthe sensor may be required in order to be able to establish the positionof the measuring body and/or the relative position of the first andsecond part during operation of the arrangement for measuringcoordinates of a work piece. It is therefore preferable to calibrate thearrangement for measuring coordinates of a work piece in relation todetermining the position of the measuring body and/or the relativeposition of the first and second part, i.e. to assign measurementsignals from the sensor to corresponding values of the position orrelative position. In the process, e.g. comparison measurements areperformed and/or use is made of calibration standards which are knownexactly in relation to the dimensions and shape and position thereofrelative to the arrangement.

Form defects, i.e. a deviation of a measuring body from an ideal orpredetermined form (e.g. spherical form or cylindrical form), can bedetermined and taken into account by calibration; in particular, theycan be corrected by calculation. Furthermore, the sensors can becalibrated, for example due to nonlinearities in the relationshipbetween the measurement signals of the sensor and the measurementvariable registered by the sensor.

If provision is/will be made for more than one sensor and/or more thanone measuring body in order to establish the position of the first orsecond part and, in particular, in order to establish the relativeposition of the first and second part, the same statements as alreadymade above apply, in particular, to the features of the sensors and/orthe measuring bodies. A plurality of sensors can be arranged either onthe first part or on the second part. Alternatively, or in additionthereto, at least one sensor can in each case be arranged on both thefirst part and the second part, which is mobile relative to the firstpart. A corresponding statement applies to a plurality of measuringbodies. A plurality of sensors can together employ at least onemeasuring body on the other part for the purposes of signal generation.However, it is also possible that a separate measuring body is assignedto every one of the plurality of sensors. Furthermore, it is possiblethat a sensor component has more than one sensor. By way of example, onesuch sensor component can therefore supply information relating to therelative position of the first and second part in relation to more thanone degree of freedom of the movement.

Supporting parts of the arrangement, which carry at least one sensorand/or one measuring body, are preferably manufactured from a materialwhich has a low coefficient of thermal expansion or coefficient ofcontraction. Furthermore, it is preferable for such supporting parts tobe embodied to be rigid against changes in shape. This also applies toan arrangement of a plurality of supporting parts. Therefore, externalforces and temperature changes do not lead to an error or lead to anegligibly small error. If the arrangement has a base, on which allother parts or most parts of the arrangement are supported directly orindirectly, for example a base plate, at least some of the sensorsand/or measuring bodies are preferably connected to the base, eitherdirectly or via such a supporting part. Exemplary embodiments will stillbe described, in which a supporting part is rod-shaped. In this case,one end of the rod is preferably attached to the base. In the case of arotational device, part of the sensor system (i.e. part of the at leastone sensor/measuring body pair), for example a sensor, is arranged onthe stationary part of the rotational device. The correspondingassociated part of the sensor system, for example an associatedmeasuring body, is preferably attached directly to the rotatable part ofthe rotational device.

The invention renders it possible, for example in the case of rotationaldevices (first aspect of the present invention) which merely enablediscrete rotational positions of the first part relative to the secondpart or vice versa, to establish the actual rotational position or toestablish a corresponding correction value, which corresponds to adeviation of the actual rotational position from the expected discreterotational position. However, as will still be explained in more detail,the invention even renders it possible to replace a rotational devicewith mechanical means for setting discrete rotational positions (e.g.with a so-called Hirth joint) with a rotational device, in which suchmechanical means are no longer present. Nevertheless, one or morepredetermined rotational positions can be set repeatedly by anappropriate control of the rotational device. In the case of anappropriate embodiment of the control, it is even possible to reproducethe rotational position exactly. To this end, the control can resort tothe measurement signals of the at least one sensor, i.e. measurementsignals or information obtained therefrom or signals are fed to thecontrol which controls the rotational movement and, in particular,controls at least one drive device (e.g. motor) of the rotationaldevice. If, for example, it is not only discrete rotational positionsthat can be set but it is also the case that the control does not enablean exact reproduction of the rotational position, the invention rendersit possible to establish the actual rotational position or to establishthe aforementioned corresponding correction value. Setting arbitraryrotational positions within a continuous range is not possible in thecase of e.g. using a stepper motor which drives the rotational movement.Such a stepper motor does not render it possible to exactly reproducespecific rotational positions either, since the rotational positionsthat can be set may be dependent on external circumstances. In addition,the drive mechanism used for the drive (e.g. with toothed wheels fortransmitting torques) may cause changes in the rotational positions thatcan be set.

In a more general case, at least one relative position is predeterminedfor the first part and the second part, which relative position is to beset during operation of the arrangement, wherein provision is made foran evaluation apparatus, which is configured to determine, usingmeasurement signals of the sensor or of sensors of the arrangement, inwhich relative position the first part and the second part are in actualfact situated when the predetermined relative position was set. Thisarrangement can, in particular, also be provided for in an embodiment inaccordance with the second aspect.

For each predetermined relative position, there may be a range ofrelative positions within which the predetermined relative position canvary, i.e. the relative position is not set exactly in accordance withthe prescription. Here, these variation ranges of relative positions forthe predetermined relative positions can, in particular, lie so farapart that they are uniquely assigned to one of the predeterminedrelative positions. By way of example, the variation ranges in respectof one degree of freedom of the movement can be separated by regionsthrough which the parts can e.g. move through, but within which they donot come to rest. In particular, for each of a plurality ofpredetermined relative positions of the first and second part,

provision can be made for at least one (individual) assigned sensor(which is assigned to the relative position), i.e. in the case of e.g.three predetermined relative positions, there are two additionalsensors, i.e. three sensors. The measuring body, which is assigned tothe additional sensor, is however also used for measuring the relativeposition in other relative positions. The measuring body is thereforearranged on one of the two parts in such a way that, in the case of therelative movement between the two parts, it reaches a position in whichit, together with the at least one assigned sensor, enables themeasurement of the relative position;

or provision can be made for at least one (individual) assignedmeasuring body (which is assigned to the relative position or elseprovision can be made for a pair or group of measuring bodies), i.e. inthe case of e.g. three predetermined relative positions, there are twoadditional measuring bodies (or pairs or groups of measuring bodies),i.e. three measuring bodies (or pairs or groups of measuring bodies).The sensor, which is assigned to the additional measuring body orbodies, is however also used for measuring the relative position inother relative positions. The sensor is therefore arranged on one of thetwo parts in such a way that, in the case of the relative movementbetween the two parts, it reaches a position in which it, together withthe at least one assigned measuring body, enables the measurement of therelative position.

In particular, there can be a plurality of assigned sensors (or aplurality of assigned measuring bodies) for at least one of thepredetermined relative positions, which plurality of assigned sensors(or plurality of associated measuring bodies) respectively render itpossible to measure the relative position in respect of one (of aplurality of different) degrees of freedom of the movement together withthe measuring body (or sensor). By way of example, there are twoassigned sensors for one of the predetermined relative positions, whichsensors measure the different degrees of freedom of the movement.

Another advantage of the present invention (second aspect of the presentinvention) consists of the fact that the actually set position and/oralignment of a probe for mechanically sensing a work piece can beestablished prior to the actual sensing process and/or appropriatecorrection information can be established in order to correct or takeinto account a position and/or alignment deviating from a prescriptionin respect of the effect thereof on the established coordinate measuredvalue or values.

A further advantage of the present invention (third aspect of thepresent invention) consists of the fact that, in the case of inadvertentmovements of the first and second part relative to one another, inparticular due to mechanical forces and/or due to thermal expansion orcontraction, the inadvertent, undesired movement can be established inrespect of the effect thereof on the relative position of the first andsecond part and hence—in the case of a CMM—on the error or the result ofthe coordinate measurement. Like in the other aspects as well, it ispossible, firstly, to undertake a correction and/or, secondly, todirectly take into account the measurement signal from the at least onesensor when determining the coordinates of the work piece. In the caseof a machine tool, the accuracy when machining a work piece is increasedwith there being little outlay for the design of the arm.

If, in accordance with the first aspect of the invention, a rotationaldevice is present and/or, in accordance with the second aspect, amovement apparatus for setting the position and/or alignment of theprobe is present, there can be a change in an elastic bending of therotational device or of the movement apparatus due to the changingweight due to a movement relative to the Earth's gravitational field (orelse due to other external influences, such as ground vibrations). Inparticular, bending can set in. It is preferable for such a change inthe bending to be taken into account. In particular, a distinction cantherefore be made between the alignment-independent and thealignment-dependent error. In order to correct this elastic deformation,use can, in particular, be made of a mathematical model which has atleast one finite element. Such a mathematical model was alreadydescribed in DE 100 06 753 A1 for correcting the elastic bending ofrotation/pivot apparatuses. The same correction is also described in thecorresponding English-language publication US 2001/0025427 A1. Asdescribed in paragraph 56 of this English-language document and asdepicted in FIG. 9 of this publication, a finite element can be treatedmathematically in such a way as if only one force vector and one torquevector acts in the center of such a finite element, with the forcevector and the torque vector being generated by the external load, i.e.the weights and optional further external forces. This model assumesthat the elastic center of the finite element, with its position andorientation in space and with its elastic parameters, contains theelastic properties of the deformed components (in this case of theelongate element). Moreover, the deformation must be linearly dependenton the loads and proportional to the forces and torques acting in theelastic center. Furthermore, the principle of superposition must hold.The finite element reacts to the force vector and the torque vector witha deformation correction vector, which is composed of a translationvector and a rotation vector. The corresponding deformation correctionvector emerges from equation 7 in the document.

In accordance with the first aspect of the invention, the first part andthe second part are parts of a rotational device, which has rotationalmobility about at least one rotational axis, wherein the first part andthe second part have rotational mobility relative to one another due tothe rotational mobility of the rotational device and wherein the firstor the second part is configured to hold either the work piece or acoordinate measuring machine, e.g. the probe or probe head, in order toenable a rotation of the work piece or of the coordinate measuringmachine. The first aspect therefore also relates to rotational devices,which have rotational mobility about two rotational axes (e.g. aso-called rotation/pivot joint with two mutually perpendicularrotational axes), or about more than two rotational axes.

In a first embodiment, the first or the second part is configured tohold the work piece. The other part is, in particular, configured to beattached to a base of the arrangement and/or to be positioned on a basesuch that this part is immobile relative to the base and the work piececan be rotated relative to the base with the other part. By way ofexample, the first and second part can be parts of a so-called rotarytable, at or on which the work piece is arranged in order to be able tobe brought into various rotational positions and in order to measure thecoordinates thereof in the various rotational positions.

In accordance with a second embodiment, the first or the second part isconfigured to hold a coordinate measuring machine. In this case, thefirst and second part enable a rotation of the coordinate measuringmachine by a relative movement. By way of example, so-calledrotation/pivot joints are known, which enable rotational mobility withrespect to two transversely and in particular orthogonally extendingrotational axes. However, rotational devices, which merely enable arotational mobility in respect of a single rotational axis or enablerotations about more than two rotational axes, are also known.

The following refinements are possible in both embodiments:

The measuring body is configured as additional material region of thefirst or second part not required for the rotational function of therotational device and/or the sensor is arranged on an additionalmaterial region of the second or first part not required for therotational function of the rotational device.

Material regions required for the rotational function of the rotationaldevice are, in particular, rotational bearings, material regions whichhold or support the rotational bearings, and also material regionsrequired for the stable rotational movement, such as e.g. a shaft or anyother rotor whose rotational movement is mounted by the rotationalbearings. Moreover, a material region which is often present andconfigured to carry and/or hold the work piece or the probe in such away that the work piece or the probe is rotated in the case of arotational movement of the part with rotational mobility, is part of thematerial regions required for the rotational function. This materialregion carries along the work piece or the probe in the case of therotational movement of the part with rotational mobility. Furthermore,the material regions required for the rotational function of therotational device include a possible material region configured toconnect the rotational device to other parts of the arrangement. By wayof example, a rotation/pivot joint is typically connected to an arm(e.g. a sleeve) of a coordinate measuring machine in order in turn to beable to pivot and rotate the probe attached to the rotation/pivot jointrelative to the arm. In the case of a rotary table, a material region istypically configured such that the rotary table can be placed onto abase of the arrangement and/or attached thereto.

By contrast, an additional material region not required for therotational function of the rotational device can form e.g. a sphericalsurface or the part of a spherical surface, a cylindrical externalsurface and/or a circular area, wherein the area formed is registered bythe sensor in terms of its position relative to the sensor. It ispreferable for the additional material region to be formed and arrangedrotationally symmetrically relative to the rotational axis, at leastover a predetermined angular range of rotational angles of therotational movement about the rotational axis, as is the case, forexample, with a semicircular disk in relation to the center of thecircle. In the case of rotational movements in the predeterminedrotational angle range, the sensor can therefore in each case register aportion of the surface of the measuring body or be influenced by themeasuring body in accordance with the relative position of theaforementioned portion of the surface in such a way that the measurementsignal generated by the sensor corresponds to the distance between thesensor and the portion of the surface. The rotationally symmetricembodiment of the measuring body surface leads to the sensor alwaysgenerating the same measurement signal or the same sequence ofmeasurement signals (e.g. in the case of measuring bodies with linegratings (see above)) in the ideal case, where the measuring body isshaped and arranged, without errors, rotationally symmetrically withrespect to the rotational axis and where the rotational movement inrespect of the rotational axis is performed without errors (e.g. wobbleerrors, axial run-out, radial run-out). Deviations from the ideal caseof the rotationally symmetric embodiment of the additional materialregion which deviations, however, are not traced back to an error of therotational axis, can be taken into account by calibration, and so acorresponding correction is possible during the evaluation of themeasurement signals from the sensor, and/or said deviations can be keptso small that the deviations of the rotational movement from the idealrotational movement bring about substantially larger changes in themeasurement signal than the deviations of the measuring body from theideal rotationally symmetric embodiment. By way of example, a sphere ora cylinder as measuring body can be produced rotationally symmetricallywith such precision and can be adjusted and/or calibrated with respectto the rotational axis with such precision that the error is small forthe purposes of determining the rotational movement error.

By way of example, the additional material region can be an elongatematerial region, which extends in the direction of the rotational axisand, in particular, is formed and arranged with rotational symmetry(that is to say e.g. cylindrically) with respect to the rotational axis.

The following refinement is based, in particular, on an embodiment ofthe rotational device, in which a rod-shaped shaft of the rotationaldevice is required for the rotational function. In particular, themeasuring body may have a greater distance from the rotational axis ofthe rotational device than a neighboring material region of the first orsecond part, which material region is required for the rotationalfunction of the rotational device, and/or the additional materialregion, on which the sensor is arranged, may have a greater distancefrom the rotational axis of the rotational device than a neighboringregion of the second or first part, which material region is requiredfor the rotational function of the rotational device.

Thus, in this refinement, an additional material region, which forms themeasuring body or on which the sensor is arranged, is arranged at agreater distance from the rotational axis than the neighboring regionrequired for the rotational function of the rotational device. Theadditional material region is rotated by a rotational movement of therotational device relative to the other part of the rotational device.As a result of the greater distance from the rotational axis, errors inthe rotational movement (i.e. deviations from an ideal rotationalmovement about a rotational axis) have a greater effect on themeasurement signal of the sensor because greater variations in therelative position of measuring body and sensor are generated at thegreater distance from the rotational axis than in the case of smallerdistances. It is therefore possible to register smaller errors in therotational movement and/or use can be made of more cost-effectivesensors with larger signal variations relative to the respective signal.

In view of a particularly stable design of the rotational device whichis particularly insusceptible to errors, a different design of therotational device is preferred than the design underlying theconsiderations in the two preceding paragraphs: at least one of the twoparts of the rotational device rotatable against one another has ahollow cylindrical shape—or has a region with this shape. At an axialend on the face of the hollow cylindrical region, there can be, inparticular, a rotational bearing, by means of which the other part ofthe rotational device is mounted in a rotatable fashion. The other partcan have any design, e.g. the shape of a circular disk. In the interiorof the hollow cylinder, in which there is no need for any parts requiredfor the rotatable function of the rotational device, there is now spacefor the measurement system. Specific exemplary embodiments will still bediscussed in the description of the figures.

In particular, the measuring body already mentioned above can be a firstmeasuring body, which is arranged on a first axial position, wherein asecond measuring body is arranged on the first or second part, at asecond axial position which is at a distance from the first axialposition. The sensor or at least a second sensor is in this caseconfigured to generate a measurement signal corresponding to a positionof the second measurement body and hence the relative position betweenthe first and second part. The axial position can be an axial positionwith respect to the rotational axis or with respect to another axis ordirection, which extends transversely or skew to the rotational axis.

By way of example, by measuring at various axial positions, it ispossible to measure wobble error due to a deviation of the alignment ofrotatable and/or rotationally symmetric parts of the rotational devicefrom the expected or desired rotational axis. Thus, in the case of awobble movement, at least one part or portion of the rotational devicerotates about the ideal rotational axis, wherein the part or portiondoes not rotate rotationally symmetrically with respect to the expectedor the ideal rotational axis as expected or as in the ideal case duringthe rotational movement. By way of example, in the case of a wobblemovement, the axis of symmetry of a cylindrical rod-shaped shaft moveson an imaginary cone surface of a cone aligned rotationallysymmetrically to the ideal rotational axis. In the case of additionaldeviations from the ideal rotational movement, further movements can besuperimposed on this wobble movement. Naturally, further errors mayoccur in addition to a wobble error, and so the axis of symmetry can, inpractice, also perform other movements. By way of example, a radialrun-out can be added to the wobble error, and so an elliptic or circularmovement not concentric with the rotational axis is superimposed on thewobble movement.

When measuring at the two different axial positions, an arrangement withat least two sensors is present at e.g. each of the two axial positions,which sensors each measure the relative position of the sensor and ofthe measuring body in various, preferably orthogonal directions, whereinthe directions can, for example, be aligned perpendicular to therotational axis.

Preferably, provision is additionally made for at least onesensor/measuring body pair (here it is possible e.g. for the samemeasuring body to interact with another sensor), which is configured tomeasure changes in the axial position between measuring body and sensor.If two such additional sensor/measuring body pairs are arranged atdifferent axial positions, it follows that it is possible to registerthe corresponding two degrees of freedom of the movement and, forexample, determine the wobble error or other errors from the totality ofthe present information. In so doing, there is no need for a separatemeasuring body to be available for each pair. Rather, the same measuringbody can be used by e.g. two sensors, a plurality of sensors or allsensors.

For many applications, one additional sensor/measuring body pairsuffices for determining the degree of freedom in the axial direction,for example if an axial relative movement of the parts overall isprecluded with high accuracy due to an air bearing, but it is intendedfor e.g. tilting movements relative to the rotational axis or axialrun-out to be registered.

It is preferable for measuring bodies and/or sensors, which are locatedat the various axial positions, to be connected to one another by meansof an element extending in the axial direction. Due to its axial length,the element can perform mechanical vibrations. Therefore, it ispreferable for provision additionally to be made for a damping apparatusfor damping mechanical vibrations of the element. This damping apparatusis preferably arranged in at least one region approximately in thecenter of the axial extent of the element. For damping apparatuses, usecan be made, in particular, of apparatuses in which damping is broughtabout due to the viscosity of a fluid. However, a damping apparatus, inwhich movements of the element generate Eddy currents such that therelative movement is braked due to the Eddy currents and hence thedesired damping effect of the vibrations occurs, is particularlypreferred. By way of example, a first part of the Eddy-current dampingapparatus is attached to the element. This first part can, for exampleproceeding from the element, extend in the radial direction, i.e.transversely to the axial direction. A second part of the Eddy-currentdamping apparatus is situated at approximately the same axial positionon the part of the arrangement movable relative to the element. Here,the first and the second part of the Eddy current damping apparatus arearranged relative to one another in such a way that movements of theelement transversely to the axial direction lead to a relative movementof the first and of the second part of the Eddy current dampingapparatus. The Eddy currents are generated during this relative movementand, as explained above, the damping effect is achieved. Alternatively,or in addition thereto, effects of vibrations of the element can bereduced or eliminated by application of a low-pass filter to the timesequence of repeatedly registered measured values of the sensors.

In particular, the aforementioned sensor can be a first sensor which isarranged at a first position in the circumferential direction in respectof the rotational axis, wherein a second sensor is arranged on the firstor second part at a second position, at a distance from the firstposition, in the circumferential direction in relation to the rotationalaxis, wherein the second sensor is also configured to generate ameasurement signal corresponding to a position of the measuring body orof a second measuring body and hence corresponding to the relativeposition of the first and second part.

Such an arrangement with two sensors, which are arranged at variouspositions in the circumferential direction with respect to therotational axis, was already mentioned above in combination withdetermining the wobble error. However, the sensors distributed in thecircumferential direction need not serve to determine the axial errors,i.e. they need not measure changes in the relative position in the axialdirection. Rather, in the case of an appropriate embodiment of thesensors (e.g. as rotational angle sensors) and also of the at least onemeasuring body (e.g. with a plurality of markings which are distributedabout the rotational axis), they can be configured to determine and/ortake into account the rotational position of a rotational device and/orthe translational relative position of two parts which have rotationalmobility relative to one another. By way of example, the alreadymentioned grating disk, in which markings on the disk, which areregistered by the sensors during a passing-by movement, are distributedon the disk in the circumferential direction with respect to therotational axis, is a suitable measuring body. Thus, a ring whichcarries the markings can also be used instead of a disk. By way ofexample, the markings are line-shaped markings extending in the radialdirection such that this can be referred to as a line grating extendingin the circumferential direction. A specific exemplary embodiment willstill be explained in more detail below.

In addition to taking account of the translational movement of parts ofa rotational device which have rotational mobility relative to oneanother, as already mentioned above, a method is proposed, whereinrotational positions of the first part relative to the second partand/or rotational positions of the second part relative to the firstpart are registered using a plurality of sensors which are arrangeddistributed about the rotational axis and, in each case, one measurementsignal corresponding to the registered rotational position is generatedso that redundant information about the rotational positions of thefirst part and second part relative to one another is available. Theredundant information about the rotational position(s) is evaluated insuch a way that effects of a translational movement of the first and thesecond part relative to one another are corrected, wherein thetranslational movement extends transversely to the extent of therotational axis.

The redundant information is redundant in respect of registering therotational position. However, it also contains information about thetranslational movement transverse to the rotational axis of therotational device.

An embodiment of a corresponding arrangement in particular comprises:

a plurality of the sensors which are arranged distributed about therotational axis and configured to in each case register the rotationalposition of the first and second part relative to one another andgenerate a corresponding measurement signal, wherein, in particular, thesensors—in axial direction of the rotational axis—are arranged on thesame side of the measuring body or on the axial position of themeasuring body,

an evaluation apparatus, which is connected to the sensors in order toreceive measurement signals from the sensors and configured to evaluaterotational positions of the first and second part relative to oneanother, as registered by the sensors, in such a way that effects of atranslational movement of the first and of the second part relative toone another are corrected, wherein the translational movement extendstransversely to the extent of the rotational axis.

In particular, the arrangement renders it possible to take into accountnot only the translational movement of the first and second partrelative to one another and, in particular, to correct this, butmoreover also renders it possible to establish the rotational positionof the first and second part relative to one another by evaluating themeasurement signals of at least one of the sensors. Therefore, onlylittle space is required for the measurement system of the arrangement.

Moreover, provision can be made for at least one sensor which isconfigured to register a distance of the measuring body from the otherpart in the axial direction of the rotational axis or, by observing themeasuring body, an axial relative position between the first part andthe second part.

As a result of the information relating to the axial distance or theaxial relative position, it is possible to take into account furtherdegrees of freedom of the movement of the rotational device and toestablish and/or correct the corresponding errors (i.e. deviations ofthe movement from an ideal rotational movement). In particular, if twoof the distance sensors or sensors for determining the axial relativeposition are available, which are directed to different regions of themeasuring body, it is possible to establish, in particular, the wobbleerror of the rotational device taking further account of measurementsignals from the rotational position sensors (i.e. using informationabout the rotational position and the translational position transverseto the rotational axis). Since the same measuring body serves to beobserved by the rotational angle sensors for registering the rotationalposition and serves to be observed by the at least one distance sensoror sensor for determining the axial position, the embodiment of themeasurement system of the arrangement is particularly space-saving. Thisapplies in particular if the rotational position sensors and the atleast one distance sensor or sensor for determining the axial positionare situated on the same side (observed in the axial direction) of themeasuring body. The measuring body can, in particular, be a disk-shapedmeasuring body, e.g. a circular disk-shaped measuring body or annularmeasuring body, which is preferably embodied and arranged in arotationally symmetric manner with respect to the rotational axis.

In a further embodiment, at least one of the rotational angle sensors isspaced from the measuring body in the axial direction and configured toprovide not only information in relation to the rotational position fromthe measurement signals thereof, but also information in respect of theaxial distance between the sensor and the measuring body; this is inplace of the distance sensor or sensor for determining the axialrelative position or in place of at least one of these. This at leastone rotational angle sensor therefore replaces the aforementionedadditional sensor. Preferably, all of the additional sensors, whichregister the axial distance or the axial relative position, are replacedby at least two of the rotational angle sensors. This saves costs foradditional sensors and even more space.

By way of example, the rotational angle sensors are embodied, as knownper se, to generate a periodic signal during the course of a rotationalmovement of the rotational device, wherein the period durationcorresponds to the time sequence of markings which reach or pass throughthe observation region or registration region of the sensor. Inparticular, it is also possible for a plurality of markings to besituated in the registration region at the same time. In this case, theperiod duration of the measurement signal corresponds to the timesequence of the markings on the measuring body entering the registrationregion or leaving the registration region.

Such a periodic measurement signal is typically sinusoidal. In place ofthe time period duration of the measurement signal, the periodicmeasurement signal can also be interpreted such that the periodcorresponds to a distance of the successive markings distributed aboutthe rotational axis in the circumferential direction.

The period or the period duration is usually used to determine therotational position or rotational speed. However, it is also possible toevaluate not only the period of the measurement signal but also theintensity of the measurement signal. In the case of optical sensors, thesensors register as primary measurement variable a radiation intensityof electromagnetic radiation (e.g. visible light or infrared radiation),which is reflected by the measuring body or passes through the measuringbody. Here, the registered radiation intensity depends on the rotationalposition. In particular, it is known that, in certain rotationalpositions, the markings on the measuring body reduce the measuredradiation intensity to virtually zero and, in other rotationalpositions, allow the measured radiation intensity to approach a maximumand, in this manner, generate the periodic measurement signal. However,corresponding effects can also be obtained using magnetic markings andmagnetic sensors. In both cases, it is possible to observe that theamplitude of the periodic measurement signal generated during arotational movement depends on the distance of the sensor from themeasuring body in the axial direction. Therefore, it is possible toidentify the distance between sensor and measuring body from theamplitude of the periodic measurement signal or else from the intensityof the measurement signal e.g. at rotational positions with maximumintensity, i.e. the distance can be determined from the amplitude orintensity of the measurement signal. Like when determining therotational position, the axial relative position or the axial distanceis naturally not determined by the sensor itself, but rather by anappropriate evaluation apparatus. This can be an individual evaluationapparatus of the sensor and/or a common evaluation apparatus of thesensors.

In order to be able to compensate for and/or correct errors of themeasuring body or the measuring bodies, errors in the arrangement,positioning and/or alignment of the measuring body or of the sensorand/or optional additional systematic errors of the at least onesensor/measuring body pair, it is proposed to provide at least oneadditional sensor (and preferably two additional sensors) at anotherposition, which at least one additional sensor generates a measurementsignal at this other position, which measurement signal is redundant inrelation to the measurement signal of the first sensor. This isunderstood to mean that, in principle, the same information is supplied,i.e. contained in the corresponding measurement signals, by both sensorsin relation to the relative position of the first and second part of therotational device. By way of example, both sensors measure the relativeposition in the axial direction parallel to the rotational axis and, inthe process, use the same measuring body, e.g. a disk arrangedrotationally symmetrically with respect to the rotational axis.Alternatively, e.g. both sensors generate a measurement signal, whichcorresponds to the relative position in a linear direction perpendicularto the rotational axis. To this end, the sensors are e.g. arrangedopposite to one another in respect of the rotational axis.

In the case of the above-described markings distributed in thecircumferential direction about the rotational axis on a measuring body,which extends about the rotational axis, the redundant information canalso be obtained by virtue of the fact that respectively one sensor isarranged at at least three different positions in the circumferentialdirection with respect to the rotational axis, which sensor detects themarkings moving past.

In any case, the redundant information can be used to reduce or evenlargely eliminate the systematic errors when measuring and evaluatingthe sensor signals.

In accordance with the second aspect of the invention, the first or thesecond part is configured to hold a coordinate measuring machineconfigured as probe for mechanical sensing of the work piece and/or asprobe head for the probe in order to enable mobility of the probe and/orthe probe head, wherein the sensor and/or the measuring body is, inaddition to determining the relative mobility of the first and secondpart, also configured to measure a deflection of the probe from aneutral position during mechanical sensing of the work piece for thepurposes of measuring the coordinates of the work piece.

The embodiment for holding a probe in particular consists of the factthat the part has an interface for attaching the probe. As known per sefrom the field of the present invention, this can be a so-calledinterchangeable interface, in which the probe can be released from thepart again and another probe can be coupled thereto.

The second aspect of the invention is based on the problem that probesfor mechanically sensing a work piece should have a mobile design forcertain measurement problems in order to align and/or position the probein different manners relative to the coordinate measuring machine. Themovement, and hence alignment and/or positioning, should be performedprior to the actual probing of the work piece. In particular, a rotationof the probe about at least one rotational axis should be possible. Tothis end, it is known to couple the probe to the coordinate measuringmachine by means of a rotation/pivot joint. In order to be able todetermine errors such as wobble errors, radial run-out and axial run-outof the rotational device, it is possible, as described above, to use oneor more sensors on the rotational device, which one or more sensorsmeasure the relative position of parts of the rotational device mobilerelative to one another in respect of at least one degree of freedom ofthe movement. As conventional in the prior art, the sensor system (atleast one sensor/measuring body pair) can in this case be arranged onthe probe side when viewed from the rotational device in order tomeasure the deflection of the probe when contacting the work piece, i.e.the probe is connected to the rotational device via the sensor system.The sensor system is e.g. a standard probe head, on which probes can beattached in an interchangeable manner (see above).

Rotational devices and sensor systems which are compact in terms oftheir dimensions are desirable; they should moreover altogether have amass which is as small as possible and should be able to be produced ina cost-effective manner.

As a solution, it is proposed to use at least one sensor or at least onemeasuring body of the sensor system, which is configured to measure themovement of the probe during mechanical probing of the work piece, andalso to measure the rotational movement of the rotational device, whichis configured to rotate the probe relative to another part of thecoordinate measuring machine.

This renders it possible to integrate sensor system and rotationaldevice into a single common device. Hence, it is possible to saveinstallation space and weight, in particular weight for housing partsand supporting parts, which carry the sensor or the measuring body.Furthermore, costs are saved for sensor and/or measuring body sincesensor and/or measuring body can be used for various measurementproblems. It is also possible to reduce the number of electricalconnection lines for transmitting measurement signals.

The methodology when operating the arrangement is e.g. as follows:initially, a desired rotational position of the probe is set by means ofthe rotational device. At least one sensor is used to establish theactual rotational position of the probe and/or an error in therotational device (e.g. wobble error, radial run-out or axial run-out).As a result, it is therefore possible to determine precisely in whichrotational position the probe is situated relative to another part ofthe coordinate measuring machine. Alternatively, or in addition thereto,the information relating to the previously set rotational positionand/or the error in the rotational device can be taken into account whenevaluating the measurement signals which are obtained during thesubsequent measurement of the work piece by mechanical sensing by meansof the probe.

In principle, it is possible to use a device as an alternative or inaddition to the rotational device, which device enables a linearmovement of the probe such that, in respect of at least one lineardegree of freedom of the movement of the probe, a position of the probecan be set. Once again, in accordance with the second aspect of theinvention, it holds true that at least one sensor or at least onemeasuring body is used both for determining the set linear position andfor measuring the movement of the probe during mechanical sensing of thework piece.

The rotational position or linear position of the probe is preferablyfixedly set prior to sensing the work piece such that the rotationalposition and/or linear position no longer changes. To this end, use canbe made of a separate locking apparatus, which e.g. causes mechanicallocking of the probe in the set position. However, it is also possibleto use merely the drive device (e.g. an electric motor), which drivesthe rotational movement or linear movement, for locking purposes (e.g.the electric motor prevents the movement when no current is flowing orprovision is made for a brake, or a closed-loop control of the motorregulates the position by appropriate actuation of the motor). In thiscase, the rotational position and/or linear position can change whilesensing the work piece. It is therefore preferable to check the setposition of the probe after sensing the work piece, when no forces aretransmitted between the probe and the work piece. To this end, use ismade of the same sensor or the same sensors, which are also used priorto sensing the work piece for determining the position or determiningthe error. If the position of the probe has changed during sensing ofthe work piece, it is possible either to correct the result of sensingthe work piece or the result can be discarded and sensing can take placeagain, for example with improved locking of the position. Alternatively,a change in the rotational position and/or the linear position can bemeasured during the sensing of the work piece and, in the process, it ispossible to use the same sensor or the same sensors which were also usedprior to sensing the work piece for determining the position ordetermining the error. In other words, if there is a sufficient numberof sensors, the position of the probe can be determined independently ofwhether a drive device or whether external forces, which for exampleoccur when probing the work piece, have led to the current position. Inparticular, in this case it is not mandatory either to register theposition of the probe prior to probing the work piece. In a furtheralternative, the position of the probe can be registered in an ongoingmanner, i.e. continuously or quasi-continuously (e.g. cyclicallyrecurrently).

It is conventional to calibrate the probe while it is attached to thecoordinate measuring machine. To this end, use is usually made of atleast one calibration body, the dimensions of which are known precisely.The results of the calibration are used when determining the coordinatesof the work piece from the measurement signals of the at least onesensor which measurement signals are generated during the sensing of thework piece. When operating rotational devices not integrated into thesensor system for measuring the deflection of the probe, it isfurthermore known to also calibrate the rotational device and, inparticular, also to calibrate the combination of rotational device andprobe. As a result of this, a set of calibration data is created in eachcase e.g. for a plurality of rotational positions of the probe, whichset is used for determining the coordinates of the work piece when theprobe is situated in the corresponding rotational position.

By integrating the movement device and the sensor system for measuringthe deflection of the probe into a common apparatus, the additionalerror sources for the exact reproduction of a rotational position orlinear position of the probe prior to sensing the work piece arereduced. By way of example, it is possible to dispense with an interfacebetween the rotational device and the sensor system. Furthermore, thenumber of signals to be transmitted can be reduced. Electricalinterfaces are dispensed with or the number thereof is reduced.Moreover, it is preferably possible to measure with the aid of thesensor/measuring body combinations in which position the probe issituated prior to sensing the work piece. It is therefore even possibleto measure whether a desired position of the probe has in fact been setor the extent to which the actually set position deviates from theintended position. It is therefore possible to correct or adapt the dataset from the calibration using the measurement signals of the at leastone sensor, which measures the actually set position of the probe priorto sensing the work piece. If such a correction or adaptation shouldlead to imprecise results of the coordinates to be determined, adecision could be made by evaluating the measurement signals of the atleast one sensor prior to sensing the work piece, that a calibration inthe set position of the probe is required. In any case, the outlay forthe change when evaluating the measurement signals for the purposes ofdetermining the coordinates is low compared to known arrangements. Theknown arrangements, e.g. as described above, comprise a rotationaldevice and a probe coupled to the rotational device by means of anadditional sensor system.

In accordance with the third aspect of the invention, the first part andthe second part are regions of the same arm of a coordinate measuringmachine or of a machine tool, which are situated at different axialpositions in the direction of the longitudinal axis of the arm, whereinthe relative mobility of the parts is a mobility due to mechanicalbending and/or thermal expansion or contraction of the material of thearm. The measuring body or the sensor is attached to a first axial endof an elongate element extending in the direction of the longitudinalaxis. The elongate element is connected to the first part at the secondaxial end thereof, which is opposite to the first end. The at least onesensor (if the measuring body is attached to the elongate element) orthe measuring body (if the sensor is attached to the elongate element)is attached to the second part. If there are a plurality of sensors, thesensors are preferably arranged on the same part.

In particular, the arrangement in accordance with the third aspect ofthe invention can comprise the following further features or anycombinations of these following further features:

-   -   The elongate element can extend within the interior of the arm.        The arm can therefore be referred to as hollow arm.    -   The arm can be the sleeve of a coordinate measuring machine,        e.g. of a coordinate measuring machine with a portal design or        gantry design.    -   Alternatively, the arm can be an arm of a machine tool, e.g. of        a robot.    -   The first axial end of the elongate element is situated in an        axial position of the arm, at which the second part is also        situated. Alternatively, the first axial end of the element can        be situated at an axial position of the arm which merely has a        small distance from an axial position of the second part. By way        of example, such a small distance is a distance corresponding to        the distance of a sensor from a measuring body assigned thereto,        wherein the sensor is e.g. attached to the first axial end of        the element and the measuring body is attached to the second        part (or vice versa).    -   The second part can comprise an interface for attaching and        connecting a probe head, a rotational device, a sensor system        with integrated rotational device in accordance with the second        aspect of the invention, or a probe.    -   The second axial end of the elongate element can be connected to        the first part at an axial position of the arm at which a        reference point of a scale for measuring the position of the arm        is also situated. By way of example, in the case of a sleeve of        a coordinate measuring machine, this position of the arm        relative to a base of the coordinate measuring machine is        displaceable, for example in the vertical direction.    -   Alternatively, the elongate element can extend over the whole        length of the arm or even beyond this in the axial direction.        The at least one sensor/measuring body pair is therefore        situated in the region of a first axial end of the arm and in        the region of the first axial end of the elongate element. In        this case, the second axial end of the elongate element is        attached to the opposite second axial end of the arm, which        forms the first part.    -   In particular, if, as in the embodiment described above, the        elongate element extends over the whole length of the arm or        else, in the general case where the elongate element can perform        mechanical vibrations due to its axial length, it is preferable        for provision additionally to be made for a damping apparatus        for damping mechanical vibrations of the elongate element. This        damping apparatus is preferably arranged in at least one region        approximately in the center of the axial extent of the elongate        element. For damping apparatuses, use can be made, in        particular, of apparatuses in which damping is brought about due        to the viscosity of a fluid. However, a damping apparatus, in        which movements of the elongate element relative to the arm        generate Eddy currents such that the relative movement is braked        due to the Eddy currents and hence the desired damping effect of        the vibrations occurs, is particularly preferred. By way of        example, a first part of the Eddy current damping apparatus is        attached to the elongate element which extends in the interior        of the arm. This first part can, for example proceeding from the        elongate element, extend in the radial direction, i.e.        transversely to the axial direction. A second part of the Eddy        current damping apparatus is situated at approximately the same        axial position on the arm, in particular on the inner side of        the wall of the arm. Here, the first and the second part of the        Eddy current damping apparatus are arranged relative to one        another in such a way that movements of the elongate element        transversely to the axial direction lead to a relative movement        of the first and of the second part of the Eddy current damping        apparatus. The Eddy currents are generated during this relative        movement and, as explained above, the damping effect is        achieved.    -   Alternatively, or in addition thereto, effects of vibrations of        the elongate element can be reduced or eliminated by application        of a low-pass filter to the time sequence of repeatedly        registered measured values of the sensors.    -   The elongate element is preferably manufactured from a material        which has a substantially smaller (in particular, smaller by at        least a factor of 100) coefficient of thermal expansion or        coefficient of thermal contraction than the material of the arm        between the first part and the second part, and preferably also        of the first and second part. Therefore, the elongate element        can be considered to be temperature stable. For this reason, it        is possible to measure the effects of the thermal expansion or        contraction of the arm with the aid of the sensor or the sensors        and the measurement body or the measurement bodies. However, a        temperature-stable elongate element is also advantageous in        that, in the case of different temperatures, the effects of the        mechanical bending due to mechanical forces acting on the arm        can be measured. Alternatively, or in addition thereto, the        temperature of the elongate element or the temperature in the        direct vicinity of the elongate element can be measured and the        effect of the thermal expansion or contraction of the elongate        element can be calculated in order to take the effect into        account when evaluating the measurement signals from the at        least one sensor.    -   It is preferable for more than one sensor to be provided for        determining the relative position of the first axial end of the        elongate element and hence, indirectly, the relative position of        the first part of the arm relative to the second part of the        arm, and for said more than one sensor to be used to determine        the relative position with respect to a plurality of the degrees        of freedom of the movement. It is preferable, at least, to        determine three degrees of freedom of the movement, namely two        linear degrees of freedom in different, preferably orthogonal,        directions, which each extend perpendicular to the longitudinal        axis of the arm, and to the linear degree of freedom of the        movement in the direction of the longitudinal axis of the arm.        If these degrees of freedom are determined, it is possible, in        particular, to measure at the axial position of the second part        of the arm in which direction and around which path the second        part has moved relative to an initial position or reference        position due to mechanical forces and/or thermal effects. In        many cases, arms of coordinate measuring machines are warp        resistant, and so further degrees of freedom of the movement,        namely rotational degrees of freedom of the movement, can be        discarded. Alternatively, the effects of a small rotational        movement of the second part can be taken into account in a        different manner, for example by calibrating a probe, directly        or indirectly attached to the second part, for mechanically        sensing a work piece.    -   If there can be a change in the alignment of the arm relative to        the Earth's gravitational field, this generally leads to a        change in the elastic bending of the arm due to the change in        direction of the acting weight. It is preferable for such a        change in the bending to be taken into account. In particular,        it is therefore possible to make a distinction between the        alignment-dependent influence due to weight, and the influence        due to other external forces and/or temperature differences. In        order to correct this elastic bending, use can be made, in        particular, of a mathematical model which has at least one        finite element. Such a mathematical model was already described        in DE 100 06 753 A1 for correcting the elastic bending of        rotation/pivot apparatuses. The same correction is also        described in the corresponding English-language publication US        2001/0025427 A1. As described in paragraph 56 of this        English-language document and as depicted in FIG. 9 of this        publication, a finite element can be treated mathematically in        such a way as if only one force vector and one torque vector        acts in the center of such a finite element, with the force        vector and the torque vector being generated by the external        load, i.e. the weight and optional further external forces. This        model assumes that the elastic center of the finite element,        with its position and orientation in space and with its elastic        parameters, contains the elastic properties of the deformed        components (in this case the elongate element). Moreover, the        deformation must be linearly dependent on the loads and        proportional to the forces and torques acting in the elastic        center. Furthermore, the principle of superposition must hold.        The finite element reacts to the force vector and the torque        vector with a deformation correction vector, which is composed        of a translation vector and a rotation vector. The corresponding        deformation correction vector emerges from equation 7 in the        document.

In particular if, as mentioned above, the second axial end of theelongate element is connected to the first part at the reference pointof a scale or at least at the axial position of the reference point, itis possible to relate the measurement results of the at least one sensorto the reference point in a direct and simple manner. By way of example,this enables a correction when calculating coordinates of a work piecemeasured by a probe with little outlay since the coordinate system ofthe scale and the coordinate system of the second part are uniquelycoupled to one another by means of the elongate element.

If the elongate element alternatively or additionally extends in theinterior of the arm, the installation volume of the arm is notincreased. Moreover, the measuring body and the sensor are preferablyarranged within the arm in this case and therefore protected fromexternal influences, without requiring an additional housing.

An advantage of the third aspect of the present invention is that thearm, e.g. the sleeve or the robot arm, does not have to be embodied tobe resistant to changes in shape with much outlay and it is hencepossible to reduce costs and weight. Rather, relative movements betweenthe first and the second part which occur can be measured and taken intoaccount. A corresponding statement applies to thermally caused changesin shape. The arm itself need not be manufactured from a material whichhas a low coefficient of thermal expansion or coefficient of thermalcontraction.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 schematically shows a longitudinal section through the end regionof a sleeve of a coordinate measuring machine, wherein a rotationaldevice for rotating a probe head (not depicted in the figure) is coupledto an end region,

FIG. 2 shows a further embodiment of an arm of a CMM,

FIG. 3 schematically shows a partial depiction of the arm as per FIG. 2,wherein sensor/measuring body pairs for measuring the bending of the armare arranged in the interior of the arm,

FIG. 4 shows an arrangement of two parts which are mobile relative toone another, wherein the arrangement comprises a measurement system formeasuring the relative position and/or relative alignment of the twoparts,

FIG. 4a shows an arrangement like in FIG. 4, wherein, however, provisionis additionally made for a rotational position sensor,

FIG. 5 shows an arrangement like in FIG. 4, wherein, however, themeasurement system is modified in respect of the design of the measuringbody or bodies,

FIG. 6 schematically shows an axial longitudinal section through a firstexample of an arrangement with a first part and a second part which ismobile relative to the first part,

FIG. 7 shows a top view in the axial direction on a variant of thearrangement in FIG. 6,

FIG. 8 shows a top view in the axial direction on a further arrangementfor measuring the position of a first part relative to a second part,

FIG. 9 schematically shows the integration of an arrangement as per FIG.4 in a rotary table,

FIG. 10 schematically shows an axial longitudinal section through asecond example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement has a measurementsystem like in FIG. 6 and/or FIG. 7,

FIG. 11 schematically shows an axial longitudinal section through athird example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement in each case has ameasurement system like in FIG. 6 and/or FIG. 7 at various axialpositions,

FIG. 12 schematically shows an axial longitudinal section through afourth example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement in each case has adifferent measurement system than in FIG. 12 at various axial positions,

FIG. 13 schematically shows an axial longitudinal section through afifth example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement in each case hasanother different measurement system than in FIG. 12 or FIG. 13, atvarious axial positions,

FIG. 14 shows a top view in the axial direction on one of themeasurement systems from the arrangement in FIG. 13, wherein themeasurement system comprises a plurality of rotational position sensorsfor measuring the relative rotational position of the two parts,

FIG. 15 schematically shows an axial longitudinal section through asixth example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement comprises a measurementsystem for determining the axial relative position of the parts,

FIG. 16 schematically shows an axial longitudinal section through aseventh example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement, in addition to thearrangement in FIG. 15, comprises a measurement system for determiningthe radial position or radial positions of the parts,

FIG. 17 schematically shows an axial longitudinal section through aneighth example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement comprises a combinationof a measurement system of the arrangement as per FIG. 13 with ameasurement system of the arrangement as per FIG. 12,

FIG. 18 schematically shows an axial longitudinal section through aninth example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement comprises a furthercombination of two different measurement systems,

FIG. 19 schematically shows an axial longitudinal section through atenth example of an arrangement with a first part and a second partmobile relative thereto, wherein the arrangement has two differentmeasurement systems like in FIG. 18, but these use a common measuringbody,

FIG. 20 shows a probe with a movement apparatus for setting the positionand/or alignment of the probe,

FIG. 21 schematically shows a perspective illustration of a probearranged on a probe head, which probe can be deflected from a restposition when probing a work piece, wherein the probe head with theprobe can be rotated about a rotational axis relative to an arm of acoordinate measuring machine and wherein both the deflection and therotation of the probe together with the probe head can be measured bythe same sensors,

FIG. 22 shows a top view on an attachment plate of the arrangement shownin FIG. 21, wherein the attachment plate has a plurality of pairs ofmagnets in order to enable the sensors to determine the respectiveposition in respect of a specific degree of freedom of the movement,

FIG. 23 shows a side view of the arrangement as per FIG. 21 in theassembled state,

FIG. 24 shows a top view on part of the attachment plate of thearrangement as per FIG. 21 to FIG. 23, wherein it is possible toidentify two pairs of magnets which are each assigned to one sensor ofthe probe head,

FIG. 25 shows a side view of an arrangement similar to the one in FIG.23, wherein the measurement of the relative position of the mobile partof the probe head and of the attachment plate is depicted for a singleor a selected degree of freedom of the movement, wherein this degree offreedom of the movement is relevant, particularly in the case of awobble movement about the rotational axis, and

FIG. 26 shows a depiction of the arrangement as per FIG. 25, likewise ina side view, wherein a deflection of the probe due to probing of a workpiece is depicted.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a sleeve 200 of a coordinate measuring machine. Asindicated by two curved lines extending approximately parallel to oneanother, the sleeve 200 can extend in the longitudinal direction thereofover a portion (not defined in any more detail). The longitudinaldirection extends from top to bottom in FIG. 1. At the free end of thesleeve situated at the bottom of FIG. 1, which free end is formed by anend region 202, a rotational device 210 is coupled in a manner known perse. The interface can be a so-called interchangeable interface, whichenables coupling of various modules, e.g., alternatively, a differentrotational device or a probe head. Therefore, appropriate electronics205 can be arranged in the end region 202, for example for identifyingand/or operating the module connected by the interface.

In a central region 201 of the sleeve 200, a scale 204, for example inthe form of a line grating which extends in the longitudinal directionof the sleeve 200, is arranged on the outside. A reference point 203 ofthe scale 204 is defined at the end of the scale 204 lying closest tothe end region 202. At the reference point 203, a bent rod 206 made of atemperature-stable material is attached directly on the inside of theexternal wall of the sleeve 200 as elongate element. Proceeding from thereference point 203, the rod 206 initially extends into the interior ofthe sleeve 200 in a direction perpendicular to the longitudinaldirection of the sleeve 200. In the further course, the rod 206 extendsin the direction of the longitudinal axis of the sleeve 200 as far asinto the end region 202. Arranged on the end region 202 is a pluralityof sensors 207 a, 207 b, e.g. capacitive sensors, i.e. sensors, thecapacitance of which depends on the relative position of a measuringbody is measured electrically. By way of example, the measuring body hasa dielectric material which is situated in the vicinity of or betweenelectrodes of the capacitive sensor.

However, other sensors, in particular the aforementioned sensors canalso be used in addition to capacitive sensors. The end region 208 atthe free end of the rod 206 serves as a measuring body. This end region208 is configured in accordance with the functional principle of thesensor 207. By way of example, in the case of a magnetic functionalprinciple, as is the case in Hall sensors or magnetoresistive sensors,the free end 208 consists of a permanent magnetic material or carries apermanent magnetic material.

FIG. 1 schematically shows a holder 209, which is attached to the end ofthe end region 202 and carries and holds the sensors 207. In the shownexemplary embodiment, it is indicated schematically that a first sensor207 a is positioned radially outside of the end region 208 of the rod206. This sensor 207 a is therefore configured to measure the relativeposition of the end region 208 and of the sensor 207 a in the radialdirection. Preferably, a further sensor (not shown) positioned radiallyoutside of the end region 208 is present, for example below or above theend region 208 in relation to the plane of the figure in FIG. 1. Thissensor can therefore be used to measure the radial distance betweensensor and end region 208 in another direction. It is optionallypossible for further sensors to be arranged at different positions inthe circumferential direction about the longitudinal axis and hencearound the rod 206. As a result, it is possible to obtain redundantinformation in relation to the position of the end region 208 of the rod206 in a plane perpendicular to the longitudinal axis of the sleeve 200or of the rod 206. It is therefore possible to eliminate systematicerrors.

A second sensor 207 b is arranged at a distance from the end region 208in the axial direction (with respect to the longitudinal axis of thesleeve 200). This sensor 207 b therefore supplies measurement signalswhich contain information about the relative position of the sensor 207b in relation to the end region 208 of the rod 206 in the axialdirection.

Instead of a sleeve, the arm depicted in FIG. 1 can also be a differentarm of a coordinate measuring machine, for example a so-calledhorizontal arm of a horizontal-arm coordinate measuring machine. In thiscase, the longitudinal axis of the arm extends approximately in thehorizontal direction. In the case of horizontal arms, the bending of thefree end of the arm depends on the weight of the devices arranged at thefree end. Using the proposed arrangement, it is possible to measure thisbending during the operation of the CMM.

In the exemplary embodiment of FIG. 1, a rotational device 210 is, asmentioned, coupled to the end region 202 of the sleeve 200 or of thearm. The stator 211 of the rotational device 210 is attached to the endregion 202 of the arm 200. By way of example, the rotor 212 of therotational device 210, depicted schematically further down in FIG. 1, isrotatably mounted by means of an annular rotational bearing 213 whichextends around the longitudinal axis of the stator 211. Atemperature-stable rod 216 is connected to the rotor 212 in arotationally secured manner and, in the longitudinal direction of thestator 211, extends into the interior thereof as far as into a region atthe interface between the arm 200 and the rotational device 210. Aplurality of sensors 217 a, 217 b is attached to the stator 211, whereinthe corresponding attachment or holder is not depicted in FIG. 1. Theend region of the temperature-stable rod 216 at the interface to the arm200 is embodied as measuring body or carries at least one measuring body218 a, 218 b. In the exemplary embodiment, these measuring bodies 218are spheres or cylinders, which are arranged in rotationally symmetricmanner in relation to the longitudinal axis of the rod 216 and hence inrelation to the rotational axis of the rotational device 210 or of therotor 212. The two sensors 217 a, 217 b, which are depicted in FIG. 1,are situated at different axial positions in relation to the rotationalaxis and are configured to measure the relative position of therespective measuring body and of the sensor in the radial direction. Atleast one further sensor is preferably arranged at each axial position,but at a different position in the circumferential direction about therotational axis such that the radial distance between the sensor and themeasuring body is measured in another direction which is preferablyperpendicular to the radial direction of the sensor 217 a or 217 b. Asalready mentioned above, provision can be made for additional, redundantsensors. The measuring body is preferably used at the respective axialposition as assigned measuring body by the plurality of sensors at thisaxial position.

In the exemplary embodiment of FIG. 1, the sensor is in each case, forboth the sensors of the arm 200 and for the sensors of the rotationaldevice 210, arranged radially outside of the measuring body providedthis is the measurement of a radial distance. In the case of the axialdistance in the direction of the longitudinal axis of the arm, thesensor is likewise, like in the case of the sensors for measuring theradial distance, arranged at the end region 202 of the arm and hence onthe movable part of the arm 200. Although this arrangement hasadvantages, particularly in respect of the electrical connections of thesensors for the purposes of measurement signal transmission to anevaluation apparatus 300 since electrical connections are generallypresent in any case at the interface between the arm 200 and therotational device 210. The sensor and the measuring body can beinterchanged however, at least in the case of one of thesensor/measuring body pairs. By way of example, at least one sensor canbe arranged at the end region 208 of the rod 206 or at the end region ofthe rod 216 in the proximity of the interface and a correspondingmeasuring body can be arranged approximately where the sensor issituated in the exemplary embodiment of FIG. 1. Alternatively, or inaddition thereto, further modifications can be undertaken. By way ofexample, the temperature-stable rod 216 of the rotational device 210can, at least in the end region thereof near the interface to the arm200, be replaced by a hollow cylinder which forms the measuring body. Inthis case, the sensors can be situated in the interior of the hollowcylinder. Furthermore, alternatively or in addition thereto, it is alsopossible to measure the axial position of the rotor by measuring theaxial position of the end region of the temperature-stable rod 216. Tothis end, a further sensor is situated within the rotational device 210,for example at a distance from the measuring body 218 b in the axialdirection.

FIG. 2 shows an arm 220 of a CMM, in particular a sleeve. This sleevecan be the sleeve 200 depicted in FIG. 1 if the probe head 221 depictedin FIG. 2 is arranged at the lower end of the sleeve and not, asdepicted in FIG. 1, a rotational device. The probe head 221 carries astylus 222 with a spherical probing element 223 at its lower end. Asindicated by a double-headed arrow, which is denoted by Z, in FIG. 2,the arm 220 can be moved particularly in the Z-direction, i.e. in avertical direction along a guide 230.

The measurement system depicted in FIG. 3, which is preferably arrangedwithin the arm 220 but can also be arranged outside of the arm, is avariant of the measurement system already described on the basis ofFIG. 1. The temperature-stable rod 226 extending in the longitudinaldirection of the arm 220 is attached with its lower end to the lower endof the arm 220. In its upper end region, the rod 226 carries twospherical measuring bodies 224, 225, which are arranged at a distancefrom one another in the axial direction. In particular, the rod 226 withthe upper end region thereof extends up to the upper end of the arm 220or even beyond the latter. As a result of this, a possible deformationof the arm 220 can be measured over the whole longitudinal extent of thelatter.

The upper sphere 224 is located, in particular, at the upper end of therod 226. An arrangement of sensors 227, 228, 229 is attached to the arm220 in the same axial region in which the upper end region of the rod226 is also situated. A first sensor 227 is aligned with the uppersphere 224 in the axial direction in order to measure the relativeposition in the axial direction. A second and a third sensor 228 a, 228b are aligned with the upper sphere 224 in the radial direction, whereinthe sensors 228 are aligned in different (e.g. orthogonal) directions inorder to measure the radial relative position in two differentdirections. A fourth and a fifth sensor 229 a, 229 b are likewisealigned in two orthogonal radial directions, but aligned with the lowersphere 225 in order to measure two mutually independent radial relativepositions at another axial position. In FIG. 3, all sensors are merelydepicted schematically by arrows which depict the alignment of therespective sensor. The length of the rod 226 and of the arm 220 is notdepicted to scale and hence is depicted schematically in FIG. 3.Compared to the width of the arm, this length can be much longer thandepicted.

Similar to the case in FIG. 3 but schematically for a general case, FIG.4 shows a measurement system with a plurality of sensors, namely fivesensors in the exemplary embodiment, which in turn are depictedschematically by arrows. Here, the direction of the arrow reproduces thealignment of the sensor, i.e. a relative position, in particular adistance between sensor and measuring body, can be measured in thedirection of the arrow. The sensors are denoted by the reference signss1, s2, s3, s4, s5, wherein, in the subsequent equations, the samereference signs s1 . . . s5 are also used for the respective measuredvalues of the sensors.

In the exemplary embodiment, provision is merely made for five sensorss1 . . . s5. Due to the design of the two parts 1, 3 mobile relative toone another and due to the connection thereof (not depicted in FIG. 4;this can be e.g. a rotatable connection or a connection which, althoughit is secure, may have a changing form due to forces and/or temperaturechanges), the information from a single sensor s1 suffices to determinethe axial relative position of the parts 1, 3 in order to determine therelative position and alignment of the two parts 1, 3 with sufficientaccuracy together with measurement results from the other sensors s2 . .. s5. In another case, there is a further sensor also aligned in theaxial direction, wherein the two sensors aligned in the axial directionand spaced apart transversely to the axial direction are in this casepreferably not arranged coaxially with respect to a possibly presentrotational axis about which the two parts 1, 3 can be rotated relativeto one another. However, such a rotational axis is not present in allcases. In particular, in the case of an arm of a coordinate measuringmachine, in which the relative movement of two different axial regionsof the arm is intended to be measured by the measurement system, no suchrotational axis is present. Naturally, this does not preclude the casewhere the two parts or regions of the arm can be rotated relative to oneanother about an imaginary rotational axis due to thermal effects and/ordue to mechanical forces. In this case, this is usually referred to astorsion. Using two such sensors aligned in the axial direction, it ispossible, in particular, to directly measure the so-called axial run-outof a rotational axis or torsion axis. The sensors can be designed andcan operate in different manners.

In the exemplary embodiment with merely five sensors s1 . . . s5 inaccordance with FIG. 4, three of the sensors s1 . . . s3 are preferablyaligned with a first measuring body K1, which is attached to the secondpart 3 of the arrangement and is spherical in the exemplary embodiment.The second part 3 carries an elongate element 4 (e.g. a cylindrical rodor a rod with a different form), on which in turn the first measuringbody K1 is attached at the free end thereof. A second measuring body K2,which in turn is spherical in the exemplary embodiment, is arranged atanother axial position of the elongate element 4 and hence at a distancefrom the first measuring body K1 in the axial direction. As analternative to a single elongate element 4, the measuring bodies can beattached to the second part 3 via several different elements or directlyto the second part. The fourth sensor s4 and the fifth sensor s5 arealigned with the second measuring body K2. Here, the second sensor s2and the third sensor s3, and also the fourth sensor s4 and the fifthsensor s5 are aligned in the radial direction, perpendicular to thelongitudinal axis of the elongate element 4. However, a preciseperpendicular alignment is only present if the longitudinal axis A1 ofthe elongate element 4 (or, alternatively, a rotational axis about whichthe parts 1, 3 can be rotated relative to one another) coincides with orruns at least parallel to the longitudinal axis A2 of the first part 1.This is not the case in the exemplary embodiment depicted in FIG. 4. Thetwo longitudinal axes A1, A2 extend skew with respect to one another orintersect. In any case, the sensors s2 . . . s5 are preferably alignedperpendicular to the longitudinal axis A2 of the first part 1.Furthermore, the pairs of sensors s2, s3 or s4, s5, which are alignedwith the same measuring body K1 or K2, are preferably aligned inorthogonal directions.

All sensors are e.g. attached to a common support 2 which in turn isattached to the first part 1. However, the sensors can also be arrangedon various supports and/or regions of the first part 1. Furthermore,there can be more than the two measuring bodies K1, K2 depicted in FIG.4. By way of example, the first sensor s1 can be aligned with adifferent measuring body than the two sensors s2, s3 aligned in theradial direction. The two sensors s2, s3 and/or s4, s5 aligned in theradial direction can also be aligned with different assigned measuringbodies.

FIG. 4a shows a variant of the arrangement shown in FIG. 4. In additionto the measurement system in FIG. 4, which enables the determination ofthe relative position of the rotatable parts in a radial position atvarious axial positions with respect to the rotational axis, provisionis made for an additional measurement system which measures therotational position of the two mutually rotatable parts 1, 3. By way ofexample, a multiplicity of markings are arranged on the second part 3,distributed about the longitudinal axis A1, such that a measuring body 9is formed. A further sensor s6 registers the markings of the measuringbody 9 when these enter a registration region of the sensor s6 or passthrough the latter. Therefore, if e.g. the parts 1, 3 perform a completerotation relative to one another about the rotational axis, the sensors6 registers all markings of the measuring body 9. As known per se, thesensor s6 can in each case e.g. generate a pulse signal whenever amarking enters the registration region or reaches or passes a specificpoint in the registration region. Alternatively, the sensor s6, forexample as likewise known per se, can in each case increase a meterreading of an incremental counter by the value 1 if it records a markingin its registration region. Other alternative embodiments of arotational position sensor for measuring the relative rotationalposition of the two parts 1, 3 are likewise possible. Furthermore, therecan also be another measurement system than the measurement systemrealized by the sensors s1 to s5, which other measurement system howeverlikewise renders it possible to register the radial position of the twoparts 1, 3 mobile relative to one another and preferably to registerthis at the axial position of the measurement system for the purposes ofmeasuring the rotational position, at least to permit the determinationof the radial relative position at the axial position of the rotationalposition measurement system. In the case of the measurement systemdepicted in FIG. 4 and FIG. 4a (and in FIG. 5), the radial relativeposition can be determined at the axial position of the rotationalposition measurement system since the measurement system measures theradial position at two different axial positions. In particular, it isnot only the radial position that is determined in one direction, butalso the relative position of the parts 1, 3 in a plane transverse tothe rotational axis.

As a result, it is now possible to correct the following effect of therotational position measurement system and thus enable a more precisedetermination of the rotational position: in the case of the rotationalmovement of the rotational device, movement components which can bereferred to as translation (i.e. linear, straight-line movement) occur.Thus, there is not an ideal rotational movement about the rotationalaxis of the rotational device, but rather there are also movementstransverse to the rotational axis and/or in the direction of therotational axis (this includes movements parallel to the rotationalaxis), at least in portions of the rotational movement about therotational axis. Such a translational movement is—depending on thedirection of this translational movement—also measured by a sensor of arotational position measurement system. If only one translationalmovement occurs, the sensor registers this movement in a manner leadingto a measurement signal which appears to indicate a rotational movementin a direction about the rotational axis. If a rotational movement and atranslational movement occur simultaneously, the sensor can generate ameasurement signal which appears to indicate a faster rotationalmovement about the rotational axis. Conversely, rotational movement andtranslational movement can also wholly or partly compensate one another,and so the sensor appears not to register any or a modified (slowed-downor reversed) rotational movement.

It is now proposed to combine the first measurement system, whichregisters the translational position and/or translational movement ofthe first and second part relative to one another, with a secondmeasurement system, which registers the rotational position of the firstand second part relative to one another. At least one measurement signalor a measured value from the second measurement system derived therefromis corrected from measurement signals and/or measured values from thefirst measurement system derived therefrom. The correction is performedin a manner such that portions of the translational movement of themeasurement signals and/or measured values from the rotational positionmeasurement system are reduced or eliminated.

A variant of the arrangement as per FIG. 4 or FIG. 4a is depicted inFIG. 5. Here, the elongate element 4 with the measuring bodies K1, K2arranged thereon is replaced by a cylindrical rod 14, which is arrangedconcentrically with the longitudinal axis A1 of the second part 3. Theend face at the free end of the cylindrical rod 14 forms a measurementarea for the first sensor s1. The cylindrical external surface of therod 14 forms a measurement area for the further sensors s2 . . . s5.

Modifications of the measurement systems shown in FIG. 4 and FIG. 5 arepossible. By way of example, the cylindrical rod 14 as per FIG. 5 neednot have a cylinder surface, continuous in the axial direction, with aconstant diameter. Rather, cylindrical regions of the rod can be formedon the axial positions at which the measuring bodies K1, K2 are situatedas per FIG. 4, wherein the rod otherwise has a different shape, e.g. hasa smaller external diameter.

The measurement signals from the sensors s1 . . . s5 can be taken intoaccount as described below in order to establish the relative positionand/or the alignment of the parts 1, 3 and/or to establish and/orcorrect a change in the relative position and/or alignment of the parts1, 3. Here, reference is made to a Cartesian coordinate system. Thesensors s2, s4 are aligned such that they measure the relative positionwith respect to the X-axis of the coordinate system; the sensors s3, s5are aligned such that they measure the relative position with respect tothe X-axis of the coordinate system, extending perpendicular to theY-axis, and the sensor s1 is aligned such that it measures the relativeposition parallel or coaxially to the Z-axis of the coordinate system,with the Z-axis extending perpendicular to the Y-axis and to the X-axis.This coordinate system is therefore a coordinate system which is basedon the second part 3. Conversely, this means that the first part 1 ismobile relative to the coordinate system and that this relative movementor the position and/or alignment relative to the coordinate system canbe determined.

From the measured values of the sensors s2, s4, it is possible tocalculate the rotational angle of the second part 3 about the X-axis(i.e. the rotational position of such a part in relation to the latter)in accordance with the following equation 1:

$\begin{matrix}{{\tan \; r_{x}} = {\frac{{s\; 2} - {s\; 4}}{d_{K\; 1K\; 2}}.}} & (1)\end{matrix}$

Here, tan r_(x) is the tangent of the rotational angle about the X-axis.d_(K1K2) is the distance between the sensors s2, s4 in the axialdirection (Z-direction), which is approximately equal to the distancebetween the first measuring body K1 and the second measuring body K2 inthe case of the exemplary embodiment in FIG. 4, provided the inclinationof the two longitudinal axes A1, A2 is small relative to one another,for example less than three degrees. Accordingly, the rotational angleabout the Y-axis can be calculated as follows from equation 2:

$\begin{matrix}{{\tan \; r_{y}} = {\frac{{s\; 3} - {s\; 5}}{d_{K\; 1K\; 2}}.}} & (2)\end{matrix}$

Here, tan r_(y) is the tangent of the rotational angle about the Y-axis.d_(K1K2) is the distance between the sensors s3, s5, which in turnapproximately equals the distance between the two measuring bodies K1,K2 or to corresponding axial positions of the rod 14 as per FIG. 5, atwhich the sensors are directed. Moreover, the translational position ofthe part 3 in respect of the coordinate system can be calculated like inthe following equation 3:

$\begin{matrix}{v_{A,B,C} = {\begin{pmatrix}{{s\; 5} + {\tan \; {r_{y} \cdot d_{K\; 1K\; 2}}}} \\{{s\; 4} + {\tan \; {r_{z} \cdot d_{K\; 1K\; 2}}}} \\{s\; 1}\end{pmatrix}.}} & (3)\end{matrix}$

Here, v_(A,B,C) is the position vector, which can also be used ascorrection vector in the case of a change in the position of the part 3relative to the part 1. The expression for calculating the X-componentof the vector is found in the first row on the right-hand side ofequation 3. The expression for calculating the Y-component is found inthe second row on the right-hand side of equation 3. The measured valuefrom the first sensor s1, which is the Z-component, is found directly inthe third row on the right-hand side of equation 3.

In the following text, an example for an appropriate correction of theerrors of the rotational device is described for the case that the parts1, 3 which are e.g. depicted in FIG. 4 and FIG. 5 and are mobilerelative to one another are parts of a rotational device, in which theparts can be rotated relative to one another about a rotational axis. Asmentioned above, the error is, in particular, the wobble error, theaxial run-out and/or the radial run-out. The correction establishes thecorrected position of a predefined location, e.g. the location of thecenter of the sphere of a probing sphere of a coordinate measuringmachine, with which the CMM mechanically probes a work piece fordetermining the coordinates of the latter, or the location of a probingpoint on the surface of a work piece, at which a CMM probes the workpiece for determining the coordinates. The predefined location isdescribed by an appropriate spatial vector, which extends from theorigin of a laboratory coordinate system to the predefined location. Thelaboratory coordinate system is a coordinate system in which a base ofthe rotational device is at rest, i.e. the part of the rotational devicewith rotational mobility is rotated relative to the base when arotational movement about the rotational axis of the rotational deviceoccurs. The part of the rotational device without rotational mobility isat rest in the laboratory coordinate system, wherein, however, elasticbending of the part without rotational mobility is, in principle, alsopossible and can, optionally, be taken into account. In order to takeaccount of the elastic deformation of parts of the rotational device or,preferably, of the whole rotational device, a mathematical model with atleast one finite element (see above) can be applied. The result of themodel is a corresponding vector which describes the bending in acoordinate system. The spatial vector p, which extends to the predefinedlocation P, can be calculated as per the following equation 4:

p=T _(P) ⁻¹ T _(A) ⁻¹(D _(A) t+v _(A))+c _(A) +b _(A)  (4).

Here, T_(P) ⁻¹ denotes the inverse matrix of the matrix T_(P) whichdescribes the inclination of the rotational device, in particular theinclination of the rotational axis of the rotational device, in thelaboratory coordinate system.

T_(A) ⁻¹ describes the inverse matrix of the matrix T_(A) whichdescribes the position of the rotational device, in particular of areference point on the rotational axis of the rotational device, in thelaboratory coordinate system. D_(A) describes the matrix which containsthe correction values due to the errors of the rotational device. Apossible composition of this matrix, from which the components of thematrix arise, will also still be considered. t denotes a vector whichextends from the aforementioned reference point of the rotational deviceto the predetermined location P. This vector t relates to a coordinatesystem in which the mobile part of the rotational device is at rest.This means that this coordinate system is rotated in the case of arotational movement of the part with rotational mobility with respect tothe laboratory coordinate system. This rotation is taken into account bythe matrix R_(A). v_(A) describes a correction vector for correctingerrors of the rotational device, namely for correcting the radialrun-out. c_(A) is a vector leading from the origin of the coordinatesystem to a reference point of the rotational device.

Finally, b_(A) in equation (4) describes a vector by means of which theelastic bending of the rotational device is taken into account. This wasalready discussed above. This vector b_(A) is e.g. the result of theabove-described correction using a mathematical model with at least onefinite element and e.g. described in equation 7 at the end of paragraph56 in US 2001/0025427 A1.

The aforementioned matrix D_(A), which is the rotation matrix forcorrecting the wobble error and the angle error of the rotationaldevice, is described by the following equation 5 in one exemplaryembodiment:

$\begin{matrix}{D_{A} = {\begin{pmatrix}1 & 0 & 0 \\0 & {\cos \; r_{x}} & {\sin \; r_{x}} \\0 & {{- \sin}\; r_{x}} & {\cos \; r_{x}}\end{pmatrix}\begin{pmatrix}{\cos \; r_{y}} & 0 & {{- \sin}\; r_{y}} \\0 & 1 & 0 \\{\sin \; r_{y}} & 0 & {\cos \; r_{y}}\end{pmatrix}{\begin{pmatrix}{\cos \; r_{z}} & {\sin \; r_{z}} & 0 \\{{- \sin}\; r_{z}} & {\cos \; r_{z}} & 0 \\0 & 0 & 1\end{pmatrix}.}}} & (5)\end{matrix}$

Here, “cos” denotes the cosine and “sin” denotes the sine of therespective angle r. As above, the label r_(y) denotes the rotationalangle about the Y-axis and the label r_(x) denotes the rotational angleabout the X-axis. The label r_(z) denotes the rotational angle about theZ-axis. The correction matrix D_(A) emerges by multiplying the threematrices on the right-hand side of equation 5.

The following equation 6 relates to the case where a probe of a CMM isarranged on the rotatable part of the rotational device:

p=T _(P) ⁻¹ T _(A) ⁻¹(D _(A)(t+Su)+v _(A))+c _(A) +b _(A)  (6).

Here, the labels already known from equation 5 have the same meaning.Equation 6 differs from equation 5 by an additional term Su, i.e. theproduct of a matrix S and a vector u. This term S is added to the vectort from equation 5. The vector u is a displacement vector which describesthe deflection of the probe from its rest position. The matrix S is thetransmission matrix of the probe which, in particular, takes intoaccount the elastic and geometric properties of the probe and can beobtained by calibrating the probe.

If, like in the second aspect of the present invention, at least onesensor/measuring body pair is used both for determining the positionand/or alignment of a probe prior to probing a work piece and fordetermining the deflection of the probe when probing the work piece, theweight of the probe also influences the position and/or alignmentthereof. Here, the influence of the weight depends on the rotationalposition of a rotational device for setting the alignment of the probeand/or depends on a linear position of a linearly mobile device forsetting the position of the probe. In particular, the influence of theweight can be taken into account by the aforementioned model with finiteelements. However, it is also possible to measure the influence of theweight using the sensors. In accordance with one preferred embodiment,sensors are therefore available for determining at least five degrees offreedom of the movement of the probe and of the rotatable part of therotational device relative to the non-rotatable part of the rotationaldevice.

FIG. 6 schematically shows an axial longitudinal section through anarrangement with a first part 13 and a second part 11, which is mobilerelative to the first part. In particular, the arrangement can be arotational device, in which the second part 11 is rotatably mountedrelative to the first part 13 about a rotational axis R extending in thevertical direction in FIG. 6.

FIG. 6 shows the measuring principle of a sensor system which comprisesa magnet 15, which is attached to the second part 11 and is preferablyarranged rotationally symmetrically with respect to the rotational axisR. Here, e.g. the north pole is situated at a higher axial position thanthe south pole with respect to the axis R. In general, it is preferablefor the longitudinal axis of the magnet defined by the two oppositepoles of the magnet to be aligned parallel to or preferably coaxiallywith the rotational axis R. In the exemplary embodiment, the second part11 moreover has an element 12 made of a magnetizable material (e.g. madeof ferromagnetic material such as e.g. ferrite), which is provided aselement for guiding the magnetic field lines as desired. The element 12is preferably formed and arranged rotationally symmetrically withrespect to the rotational axis R. At the one pole of the magnet 15 (inthis case the north pole), it has a disk-shaped region which extends inthe radial direction with respect to the rotational axis R. At theexternal circumference thereof, a cylindrical region extends coaxiallywith respect to the rotational axis R in the axial direction, parallelto the longitudinal axis of the magnet 15 and hence in the direction ofthe axial position of the other magnetic pole (in this case the southpole) of the magnet 15. At the end of the cylindrical region, a furtherradially interior region of the element 12 may optionally be present (asdepicted in FIG. 6), and so the remaining annular gap between theradially interior region 16 and the magnet 15 is smaller than betweenthe cylindrical region and the magnet 15. At least one sensor 14—twosensors 14 a, 14 b in the exemplary embodiment—for measuring the radialposition or relative position of the first part 13 and of the secondpart 11 is situated in this annular gap. The at least one sensor 14 isattached to the first part 13, for example by means of a support 17extending parallel to the rotational axis R. In the exemplaryembodiment, the two sensors 14 a, 14 b are arranged at radial positionswhich are opposite to one another with respect to the rotational axis R.Hence, these are sensors which supply redundant information in relationto the relative position of the first part 13 and of the second part 11;to be precise, in a direction which extends in the horizontal directionin the plane of the figure in FIG. 6.

A flux guiding part (e.g. made of ferrite) can optionally also besituated at the lower magnetic pole of the magnet. By way of example,the sensor can be a Hall sensor or a magnetoresistive sensor.

FIG. 7 shows a variant of the arrangement of FIG. 6, with the view beingdirected in the axial direction of the rotational axis R from FIG. 6; tobe precise, directed to the lower side of the magnet 15 and of theelement 12. In the annular gap between the radially interior region 16and the magnet 15, there are two additional magnetic sensors 14 c, 14 din addition to the two sensors 14 a, 14 b depicted in FIG. 6. However,observed in the circumferential direction about the rotational axis R,these further sensors 14 c, 14 d are at a different position, and sothey measure the relative position of the first part 13 (not shown inFIG. 7) and of the second part 11 in a different direction than thesensors 14 a, 14 b. In FIG. 7, the direction in which the sensors 14 a,14 b measure the relative position is denoted by X since this may bee.g. the direction of the X-axis of a Cartesian coordinate system. TheY-direction extending perpendicular thereto is the direction in whichthe sensors 14 c, 14 d measure. In FIG. 6, the X-direction extends fromright to left.

FIG. 8 shows a variant of an arrangement for measuring the position of afirst part 23 relative to a second part 21. The figure shows a sectionthrough the arrangement transversely to a rotational axis R, about whichthe parts 21, 23 have rotational mobility relative to one another. Fromthe view of the rotational axis R, magnets 25 a, 25 b are arranged onthe first part 21 in different, preferably orthogonally extending radialdirections. Contrary to what is depicted in FIG. 8, the magnets 25 canalternatively be arranged at a relatively large distance from therotational axis R, namely at a distance which approximately equals thedistance of sensors 14 which sensors are attached to the second part 21.Overall, eight sensors 14 are arranged on the first part 23, whichsensors are assigned to the magnets 25 a, 25 b; i.e., the sensors 14 canin any case measure the position of said magnets in the radialdirection, i.e. perpendicular to the rotational axis R, when the magnets25 a, 25 b are in the vicinity thereof. The magnets 25 a, 25 b thereforeexert the function of measuring bodies which are assigned to the sensors14 a to 14 h. These sensors 14 are distributed over the circumference ofthe first part 23 with the same angular distances in relation to therotational axis R. Thus, in the case of eight sensors 14, a sensor issituated every 45° in the circumferential direction. If the sensors 14and the magnets 25 are situated at the same distance from the rotationalaxis R, the sensors and magnets are offset from one another in the axialdirection, i.e. parallel to the axis R, so that the rotational movementabout the rotational axis R is possible.

The arrangements in accordance with FIG. 8 are an alternativerealization of a sensor system to the measurement system depicted inFIG. 4 and FIG. 5. In particular, the sensors s2, s3 or the sensors s4,s5 can through it, s5 with the respective assigned measuring body can bereplaced by the arrangement in accordance with FIG. 8. This also meansthat, in each case, an arrangement in accordance with FIG. 8 can replacethe arrangement of the sensors s2, s3 or s4, s5 with the assignedmeasuring body. In this case, the two arrangements in accordance withFIG. 8 are situated at different axial positions with respect to therotational axis R. It is additionally possible, as shown in FIG. 4 andFIG. 5, for e.g. at least one sensor s1 to be present, which measuresthe axial relative position of the parts mobile relative to one another.

The arrangement in FIG. 8 can be modified, in particular by virtue ofthe two magnets 25 a, 25 b being replaced by one sensor in each caseand, accordingly, the eight sensors each being replaced by one magnet.Furthermore, it is possible to use other sensors than magnetic sensors,e.g. capacitive or inductive sensors with appropriate assigned measuringbodies. Alternatively, or in addition thereto, it is possible to varythe number of sensors 14. By way of example, it is possible that merelyfour sensors, or else sixteen sensors, are distributed over thecircumference.

The embodiment as per FIG. 8 renders it possible, particularly in thecase of specific rotational positions of the first part 23 relative tothe second part 21, to measure the two radial positions. In thesespecific rotational positions, the magnets 25 are each situated in thevicinity of one of the sensors 14 such that the measurement of theradial relative position succeeds with high accuracy. Thus, thearrangement in accordance with FIG. 8 renders it possible to establishthe errors of the rotational device (in particular wobble error) atthese specific rotational positions. In particular, in the case ofcoordinate measuring machines with probes or probe heads which arerotatable with respect to an arm of the CMM, a plurality of discreterotational positions are often sufficient to satisfy the measuringproblems in a suitable manner, and a corresponding statement applies toa rotary table on which a work piece can be arranged in a rotatablemanner relative to a base of the rotary table. In the case of aplurality of discrete rotational positions of the work piece relative tothe base, e.g. the eight different rotational positions in accordancewith the arrangement from FIG. 8, the work piece can be machined and/ormeasured as desired.

The principle of the arrangement in accordance with FIG. 8 can also beapplied to an arrangement similar to the one as per FIG. 6, i.e. thesensors being arranged in a gap between a permanent magnet and anotherpermanent magnet or in a gap between a permanent magnet and an elementfor magnetic flux guidance or in a gap between two elements for magneticflux guidance.

In particular, it is possible to successively query the signals from theplurality of sensors 14 as per FIG. 8 (or another number of a pluralityof sensors) in a cyclic or other manner by means of a multiplexer andhence register these. By way of example, in the angular position shownin FIG. 8 between the two parts 21, 23 which are rotatable with respectto one another, only the measurement signals from the sensors 14 a, 14 gwould assume values providing information about the radial relativeposition.

It applies in general and not only in the embodiment of FIG. 8 that e.g.analog electrical signals from a sensor can be digitized by ananalog/digital converter and that the signals can subsequently beprocessed digitally, in particular by using a computer.

The principle explained on the basis of FIG. 4, according to which theerror of the rotational device can only be measured at specific discreteangular positions (or in narrow ranges about these discrete angularpositions) is however also advantageous in that these discrete angularpositions can be determined by means of the same sensors that are alsoused to determine the error of the rotational device. As mentionedpreviously, e.g. only the sensors 14 a, 14 g emit measurement signalswhich make it possible to deduce the vicinity of a magnet 25 in therotational position depicted in FIG. 8. Hence, the left-hand positioncan be established uniquely from the signals of the sensors. The exactposition and alignment can then be established by means of sensors 14 a,14 g (or by other sensors 14 in the case of other angular positions orrotational positions) and optionally by further sensors for determiningthe radial relative position at a different axial position andoptionally by at least one additional sensor for determining the axialposition. If the angular position is not or cannot be established usingthe same sensors as for determining the errors of the rotational device,use is preferably additionally made of a further measurement system,which is configured to establish the angular position or rotationalposition. Such systems are known from the prior art and will not bedescribed in any more detail herein.

FIG. 9 schematically shows the integration of an arrangement as per FIG.4 into a rotary table. The rotatable part 33 of the rotary table serves,in particular, to arrange a work piece on the rotary table 33. The baseof the rotary table is connected to or formed by the non-rotatable part31. The part of the measurement system which carries the measuringbodies K1, K2, e.g. like in FIG. 4 on a rod 34, is attached to the lowerside of the rotatable part 33 and is also moved in the case of arotational movement of the rotatable part 33. The rod 34 with themeasuring bodies K1, K2 extends from top to bottom in the interior ofthe non-rotatable part 31. Like in FIG. 4, the sensors s2, s3, s4, s5are indicated schematically by arrows and are attached to thenon-rotatable part 31.

In place of the measurement system in accordance with FIG. 4 and FIG. 9,it is also possible for a different measurement system to be integratedinto the rotary table with the parts 31, 33 that are rotatable withrespect to one another. In particular, the sensors can co-rotate withthe rotatable part 33 and the measuring bodies can be arranged on thenon-rotatable part 31. Furthermore, it is possible to use othermeasuring bodies than the spherical measuring bodies K1, K2. By way ofexample, the measurement system in accordance with FIG. 8 can also beintegrated into the rotary table in accordance with FIG. 9. Furthermore,it is possible that, in a similar manner, a measurement system is notintegrated into a rotary table but rather into a rotational device forrotating a probe of a CMM or for rotating a tool of a machine tool. Inthis case, the measurement system, as depicted in FIG. 9, is likewisesituated within one of the two parts that are rotatable with respect toone another.

FIG. 10 shows a measurement system as in FIG. 6 and/or FIG. 7. For thecorresponding parts of the measurement system, use is made of the samereference signs as in FIG. 6 and FIG. 7. However, alternatively, use canalso be made of a different measurement system, for example similar toone schematically depicted in FIG. 4 and FIG. 5. This also applies tothe embodiments depicted in the following figures.

The embodiment as per FIG. 10 has a rotatable part 41, which is securelyconnected to the part 11 of the measurement system. The sensors 14 a, 14b of the measurement system are connected to a non-rotatable part 43,i.e. the rotatable part 41 can be rotated relative to the non-rotatablepart 43 about the rotational axis R, wherein the rotation also resultsin a different rotational position of the element 12 of the measurementsystem relative to the sensors 14. However, these sensors 14 are notconfigured to establish the rotational position. However, this would bethe case e.g. when using a measurement system in accordance with FIG. 8(see above).

The arrangement in accordance with FIG. 10 enables the calibration ofthe measurement system since the position of the rotatable part 41, andhence of the parts of the measurement system connected to the part 41,can be changed in the radial direction relative to the rotational axisR. To this end, the rotatable part 41 is attached to an intermediatepart 45 by means of attachment means, screws 46 a, 46 b in the exemplaryembodiment. This intermediate part 45 is rotatable about the rotationalaxis R and, for this purpose, is mounted on the non-rotatable part 43 bymeans of a rotational bearing 44. Stated more generally, thenon-rotatable part 43 is rotatably coupled to a first rotatable part 45by means of a rotational bearing 44 such that the first rotatable partand the stationary part 43 can perform a rotational movement relative toone another about a rotational axis R. A second rotatable part 41 issecurely but detachably connected to the first rotatable part 45 suchthat the relative position of the first rotatable part 45 and of thesecond rotatable part 41 can be set.

In respect of the calibration of the sensors 14, which enable ameasurement of the relative position of the stationary part 43 and ofthe rotatable part 41, the second rotatable part 41 is affixed invarious relative positions in the radial direction relative to the firstrotatable part 45 (in particular by detaching and re-affixing thefixation means, changing the relative position and re-affixing thefixation means). In all these relative positions of the parts 45, 41,measured values of the corresponding sensors assigned to this degree offreedom of the movement or measured values of the sensor are establishedand calibration information is obtained therefrom. If the relativeposition of the non-movable part 43 subsequently changes relative to thesecond movable part 41 due to errors (in particular wobble errors) ofthe rotational device, it is possible to establish in which relativeposition the parts 41, 43 are situated by means of the obtainedcalibration information. In particular, nonlinearities between therelative position and the sensor signal of the respective sensor areestablished by the calibration.

For other degrees of freedom of the movement, it is also possible thatthere is a corresponding movement possibility between a first and asecond rotatable part such that these two rotatable parts can be affixedwith respect to the degree of freedom of the movement in differentrelative positions.

As an alternative or in addition to calibration by means of a change inthe relative position of two parts with rotational mobility, the sensorscan be calibrated in a special measurement arrangement, i.e. the sensorsare then not situated in the rotational device but rather in a referencerotational device or in another special design for calibration. Afterthe calibration values have been obtained, the sensors are inserted intothe rotational device and supply measured values during the operation ofthe rotational device. A corresponding statement also applies e.g. ifthe sensors are not inserted into a rotational device but rather intothe above-described arm of a CMM or of a machine tool in accordance withthe third aspect of the present invention.

If at least two measurement systems or partial measurement systems arearranged for registering the radial relative position at different axialpositions in respect of the rotational axis, a non-parallel alignment ofthe two measurement systems or partial measurement systems is preferablyalso established and/or corrected by calibration. The eccentricity ofthe measurement systems or partial measurement systems with respect tothe rotational movement about the rotational axis is preferably alsoestablished and/or corrected by calibration. Once again, it is possibleto establish the error of the whole measurement system or of bothmeasurement systems in a separate calibration arrangement. To this end,the two measurement systems or partial measurement systems are securelyconnected to one another and operated in a reference rotational device,which has a negligibly small or exactly known error of the rotationalmovement; i.e., appropriate measured values of the sensors are recordedin various rotational positions of the reference rotational device.Subsequently, the arrangement of the measurement systems or partialmeasurement systems is inserted into the rotational device, in which thesensors are to continuously supply signals during operation. Here, thesecure connection between the two measurement systems or partialmeasurement systems is not modified relative to the use in the referencerotational device.

FIG. 11 shows two of the measurement systems in accordance with FIG. 6and FIG. 7, wherein the measurement systems can once again be replacedby other measurement systems. However, in the special exemplaryembodiment, merely one sensor is depicted for determining the radialrelative position of the part 51 with rotational mobility relative tothe part 53 without rotational mobility. In the bottom one of the twodepicted measurement systems, there is additionally also a sensor 19 formeasuring the axial relative position of the parts 51, 53, wherein thissensor 19 is arranged at a small distance from the lower magnetic pole(in this case south pole) of the measurement system depicted furtherdown.

In the exemplary embodiment, the stationary part 53 (the stator) isU-shaped in the depicted longitudinal section and contains in theinterior thereof the lower measurement system and a connection 59between the lower and the upper measurement system. As a result of this,both measurement systems are co-rotated in the case of a rotationalmovement of the rotatable part 51. However, the parts of the measurementsystem connected to the stator 53 (in this case the sensors) arenaturally not co-rotated. The stator 53 and the movable part 51 are inturn mounted on one another in a rotatable manner by means of arotational bearing 44. A drive for a rotational movement of therotatable part 51 is depicted schematically top-left in FIG. 11. A motor54 drives a rotational movement of a drive shaft 58, by means of which adrive wheel (e.g. a friction wheel or toothed wheel 57) is rotated,which transmits a corresponding torque to the rotatable part 51. FIG. 11does not, for each of the two measurement systems, depict in each case apreferably additionally present second sensor for measuring a radialrelative position of the part 51 with rotational mobility and of thestator 53 in a direction extending perpendicular to the first radialdirection, in which the sensors 14 a and 14 b depicted in FIG. 11measure the radial relative position.

FIG. 12 shows an arrangement like in FIG. 11, wherein, however, the twomeasurement systems are replaced by another measurement system whichcorresponds to the embodiment described on the basis of FIG. 4. Attachedto the rotatable part 51 is a rod-shaped support 4, which extendsrotationally symmetrically with respect to the rotational axis R fromtop to bottom in the interior of the stator 53. The rod-shaped support 4carries two spherical regions K1, K2 as measuring bodies at an axialdistance with respect to the rotational axis R. Directed on the stator53 are the sensors 64 a, 64 b, 69 and two additional sensors fordetermining the radial distance in a different direction than thesensors 64 a, 64 b. Here, the sensor 69 for determining the axialdistance of the stator 53 from the spherical measuring body K1 iscarried by the base of the stator 53 situated at the bottom. Aconnection cable 63 a of the sensor 69 is passed from top to bottomthrough the base of the stator 53. By means of the cable 63, the sensorsignal from the sensor is fed to an evaluation apparatus (not depictedhere). The two sensors 64 a, 64 b, which are directed to the firstspherical measuring body K1 or the second spherical measuring body K2,are attached to a sidewall (i.e. a longitudinal limb of the U-profile inthe depicted longitudinal section). In each case, a connection cable 63b, 63 c is again passed through the sidewall of the stator 53, whereinthe cables 63 are likewise connected to the evaluation apparatus. Thesensors 64, 69 are e.g. optical sensors. Alternatively, these can bee.g. capacitive sensors. In this case, the measuring bodies K1, K2 aremade of e.g. electrically conductive material, e.g. steel.

FIG. 13 shows a stator 53 and a rotor (rotatable part) 51 like in FIG.11 and FIG. 12, which are likewise rotatably mounted by means of arotational bearing 44. However, the measurement systems from FIG. 11 andthe measurement system from FIG. 12 have been replaced by anothermeasurement system. A rod-shaped support 73 protrudes downward from therotor 51 into the cavity of the stator 53, wherein the rod-shapedsupport 73 is attached to the rotor 51 in a rotationally secured mannerand arranged coaxially with respect to the rotational axis R. Atdifferent axial positions in relation to the rotational axis R, the rod73 respectively carries a disk 75 a, 75 b, which, e.g. as shown in FIG.14, has a structure with a multiplicity of markings which are arrangedat a distance from one another on the disk or by the disk. Thesemarkings spaced apart from one another can therefore be referred to as agrating and, in the case of line-shaped markings, as a line grating.Here, the markings, of which some are labeled with the reference sign 82in FIG. 14, preferably extend along a circular line, i.e. the distancefrom one another corresponds to the corresponding section of thecircular line between the markings. Here, the circular line extendsaround the rotational axis R. Like FIG. 7, FIG. 14 also depicts thetransversely and respectively orthogonally extending X- and Y-axes, inthe direction of which the relative positions of the stator and of therotor are to be determined.

While the sensors 74 a, 74 b and 74 c, 74 d for measuring the radialrelative position are arranged opposite to one another with respect tothe rotational axis R in the radial direction or diameter direction, thearrangement of the sensors 74 a, 74 b, 74 c, 74 d, 74 e which is shownin FIG. 14 has a different design. The top view of FIG. 14 shows that atotal of five sensors 74 are distributed approximately uniformly overthe circumference. Hence, none of the sensors 74 in FIG. 14 lie directlyopposite another sensor with respect to the rotational axis R.

In any case, the sensors 74 in accordance with FIGS. 13 and 14 aredesigned to establish not only the rotational position or change inrotational position of the disk 75 with respect to the rotational axisR, but also the radial position of the disk 75 relative to the sensorsand hence the radial position of the rotor 51 relative to the stator 53.Here, it is not mandatory for the signals of the individual sensors tobe evaluated and a radial position to be established therefrom in eachcase in relation to the connection line between the sensor and therotational axis R. Rather, the position of the disk 75 and hence of therotor 51 within the plane which extends perpendicular to the rotationalaxis R and is defined by the disk can be determined from the totality ofthe signals from more than one of the sensors 74. In order to determinethis position in the plane or the individual radial relative position,use is made of the effect that the distance between linear markings 82,which extend in the radial direction and therefore perpendicular to theaforementioned circular line, increases with increasing distance fromthe rotational axis R and becomes smaller in the opposite direction. Asa result, this also changes the measurement signal from the sensors 74,which sensors simultaneously register a plurality of markings.

As shown in FIG. 13, the sensors 74 are once again attached to the innerside of the sidewall of the stator 53. Suitable sensors are described ine.g. EP 1 923 670 A1.

FIG. 15 shows a variant of a partial measurement system for determiningthe axial relative position with respect to the rotational axis R. Thearrangement of stator 53, rotational bearing 44 and rotor 51 is embodiedas in FIG. 11 to FIG. 13. However, the height of the sidewalls of thestator 53 and hence the height of the interior thereof can vary. Thisalso applies to embodiments other than the one depicted in FIG. 15. Amagnetic sensor 89 is securely connected to a sidewall of the stator 53by means of a support 87. Said sensor is situated in the region of therotational axis R, i.e. it is pierced by the imaginary rotational axisR. A first magnet 85 b, which is securely arranged on the underside ofthe rotor 51 by means of a rod-shaped support 84, is situated at anaxial distance above the sensor 89. A second magnet 85 a is arranged atan axial distance below the sensor 89 and likewise attached to thestator 53, like the sensor 89. Due to the two magnets 85, a particularlystrong magnetic field is generated at the location of the sensor 89,such that the spatial resolution is particularly high when measuring theaxial position. However, the lower magnet 85 a is not mandatory. By wayof example, in the embodiment of FIG. 11, which was described above, thesensor can be attached directly to the lower part of the stator 53 andthe lower magnet 85 a in accordance with FIG. 15 can be dispensed with.

A similar design to FIG. 15 is shown in FIG. 16, wherein, however,provision is additionally made for a measurement system for determiningthe radial position or radial positions of the rotor 51 relative to thestator 53. By way of example, the additional measurement system isembodied as already described on the basis of FIG. 13 and FIG. 14. Adisk 75 with a multiplicity of spaced-apart markings is arranged on arod-shaped support 84, rotationally secured with respect to the rotor51. At least two sensors 74 a, 74 b for registering the spaced-apartmarkings by or on the disk 75 are fixedly connected to the sidewalls ofthe stator 53. The overall arrangement of the sensors of the embodimentin FIG. 16 serves to establish three degrees of freedom of the movement,with it not being possible to record drum errors. The arrangement istherefore suitable for rotational devices, in which wobble errors arenegligibly small, for example due to the design. The advantage of thearrangement as per FIG. 14 lies in the small installation height, i.e.in the small extent along the rotational axis R.

FIG. 17 shows a combination of the upper measurement system from thearrangement in accordance with FIG. 13 with the lower measurement systemfrom the arrangement in accordance with FIG. 12. The same referencesigns as in FIG. 12 and FIG. 13 have the same meaning in FIG. 17. It ispossible to establish linearly mutually independent radial relativepositions of the rotor 51 and of the stator 53 at a first axial positionwith respect to the rotational axis R using the two sensors 74 a, 74 band the disk 75. It is possible to establish two radial, mutuallyindependent radial relative positions of the stator 53 and of the rotor51 at a second axial position of the rotational axis R using the sensor64 a and a further sensor (not depicted here), which are aligned withthe measuring body K1, which is arranged on the rod-shaped support 73 inthe lower end region thereof. An axial relative position of the sphereK1 and of the sensor 69, which is attached at the bottom to the stator53, can additionally be established.

FIG. 18 shows a further combination of two different measurement systemsor partial measurement systems. The stator 53, the rotational bearing44, the rotor 51 together with the downwardly protruding rod-shapedsupport 73 and the upper partial measurement system with the disk 75 areembodied as in FIG. 17 or as in FIG. 13 and FIG. 14. The lower secondpartial measurement system, arranged at a different axial position ofthe rotational axis R, however has a different design than in FIG. 13and FIG. 17. It has a cylindrical disk 95, on the outer edge of whichextending in the circumferential direction a first sensor 64 a isaligned for establishing the radial relative position between thecylinder disk 95 and the stator 53. Furthermore, two sensors 94 a, 94 baligned in the axial direction, i.e. parallel to the direction of therotational axis R, to a planar surface of the cylinder disk 95 areconnected to the stator 53. These two sensors 94 enable not only thedetermination of the axial relative position between the cylinder disk95 and hence, firstly, the rotor 51 and, secondly, the stator 53, butalso the determination of the wobble error. This embodiment isadvantageous in that only a small number of sensors 74 is required onthe upper partial measurement system. However, in order to register theposition of the disk 75 in the plane extending perpendicular to the axisR, the information of at least two sensors 74 which do not lie oppositeto one another with respect to the rotational axis R is required.

An embodiment with a particularly low installation height, i.e. theextent along the rotational axis R is particularly small, is depicted inFIG. 19. Once again, there is a measurement system with a disk 75arranged on the rod-shaped support 73 of the rotor 51, which diskcarries a multiplicity of markings. However, the assigned sensors 74,which measure the relative position of the disk 75 with respect to twomutually independent radial relative positions, are arranged on the oneaxial side (namely the top in FIG. 19) of the disk 75. On the oppositeaxial side of the disk 75, namely the bottom in FIG. 19, two sensors 94a, 94 b are arranged in the lower partial measurement system, like inFIG. 18. These sensors 94 are aligned parallel to the rotational axis R.Once again, these two sensors 94 enable the determination of the axialrelative position of stator 53 and rotor 51, and also the determinationof the axial run-out.

In particular, the sensors 74 can, as described above, also be used todetermine the translation movement or the translational positiontransversely to the direction of the rotational axis R. In this case,the arrangement can also determine the wobble error.

In the case of a variant not depicted in FIG. 19, the sensors 94 can bedispensed with and the rotational angle sensors 74 are moreoverconfigured to measure the axial relative position between the measuringbody 75 and the sensors 74. The sensors 74 therefore assume the functionof the sensors 94. This variant can have an even lower installationheight since e.g. the measuring body 75 can be positioned even closer tothe floor of the stator 53. However, they can also have an installationheight that is just as low (in the axial direction) if the sensors 94are situated on the same axial side of the disk 75 as the sensors 74.

The embodiment schematically depicted in FIG. 20 is configured inaccordance with the second aspect of the present invention. Depicted isa stylus 122 for mechanically sensing a work piece, the coordinates ofwhich are to be determined. The stylus 122 has a probing sphere 123 oranother probing element at the free end thereof. As indicated by twoconcentric circles, the stylus 122 is movably mounted (bearing 120), inorder to be able to be deflected from its rest position when sensing thework piece. This deflection is measured in a conventional manner and thecoordinates of the respective probed point on the surface of the workpiece are determined therefrom. To this end, the stylus is combined witha sensor system which is depicted schematically in FIG. 20 by twosensors s1, s2. In the exemplary embodiment, the sensors s1, s2 arerigidly (i.e. without the option of a relevant relative movement)connected to the stylus 122, while the associated measuring bodies areconnected rigidly to the holder of the stylus or of the probe head, inparticular to an arm of a CMM. Both when deflecting the stylus 122 whenprobing a work piece and when setting the position and/or alignment ofthe stylus prior to or during the probing of a work piece, there is arelative movement between the stylus 122 and a support 115 of themeasuring bodies, and hence also a relative movement between the sensorsand the measuring bodies.

In FIG. 20, a plurality of measuring bodies M1 to M5 are depicted on thesupport 115 or on the non-movable part. This will be discussed in moredetail below. This plurality of measuring bodies M1 to M5 is assigned tomerely one of the sensors, namely the sensor s1. Corresponding measuringbodies assigned to the other sensor s2 or optional further sensors arenot depicted in FIG. 20 since this is a schematic illustration. However,it is also possible that at least one measuring body is arranged on thestylus and a plurality of sensors is arranged on the non-movable part ofthe arrangement.

In addition to the mobility due to the bearing 120, the stylus 122 canbe rotated about a rotational axis R together with the sensors (ormeasuring bodies) securely connected thereto. This occurs in particularfor the purpose that the stylus 122 is to be aligned differently priorto probing a point on a surface of the work piece. The dashed linesdepict a different rotational position of the stylus and of the sensors,into which position the stylus 122 has been brought by rotation aboutthe rotational axis R. It is possible to identify that, with this, thebearing 120 has also rotated. Subsequently, a work piece can be probedin this modified alignment of the stylus 122. However, the position oralignment of the non-movable part 115 of the arrangement with themeasuring bodies M1 to M5 attached thereto is not changed by therotation about the rotational axis R. Other than depicted in FIG. 20,the rotational axis R preferably intersects a fixed point of the bearing120.

The sensors and the associated measuring bodies of the arrangement are,in accordance with the second aspect of the invention, arranged in sucha way that it is possible to establish firstly the change in thealignment of the stylus 122 due to the rotation about the rotationalaxis R (or the rotational position about the rotational axis R) from thesensor signals, and secondly the deflection of the stylus 122 whensensing or probing a work piece in the respective alignment. Anarrangement with a plurality of measuring bodies and a common sensorassigned to the measuring bodies or, conversely, with a plurality ofsensors and a common measuring body assigned to the sensors can,however, also occur in other cases, in which merely the relativeposition of the first and second part of the arrangement is intended tobe measured, but no additional mobility of a stylus or another probe.

By way of example, the measuring bodies M1 to M5 can be magnets and thesensor S1 can be a magnetic sensor, e.g. a magneto resistive sensor or aHall sensor. When carrying out the rotational movement about therotational axis R, the measurement signal of the sensor s1 can berecorded continuously and/or repeatedly. From this, it is possible toestablish the covered rotational angle with respect to the rotationalaxis R or at least one component of the rotational angle since, when thesensor s1 moves along the various measuring bodies M1 to M5, themeasurement signal is changed in a characteristic manner; in particular,the magnetic field at the location of the sensor s1 becomes stronger andweaker in a cyclical manner.

When the stylus 122 is deflected, the sensors s1 in turn moves relativeto at least one assigned measuring body, wherein the relative movementof the sensor s1 relative to the measuring body in general proceedsdifferently than in the case of a rotational movement of the stylus 122about the rotational axis R. This means that, optionally, even moremeasuring bodies can be assigned to the respective sensor s1, s2, whichare not required when following the movement about the rotational axisR. However, the signals of the various sensors s1, s2 during thedeflection of the stylus 122 are used in any case to establish thedirection and the path by which the stylus 122 was deflected from itsrest position.

In any case, it is an advantage of the depicted arrangement that atleast part of the sensor system can be used both for following themovement or determining the rotational position of the stylus withrespect to a rotation about the rotational axis R, and also fordetermining the deflection of the stylus when probing a work piece.

FIG. 20 merely serves for visualizing the principle. Therefore,variations are possible. By way of example, this need not be a stylus,but rather it is possible to provide a different probe for mechanicallyprobing a work piece. In addition, other movement options of the probemay be given, e.g. merely a linear movement option, or the probe canhave two or more rotational degrees of freedom of the movement. Therecan also be an additional linear movement option. This plurality ofdegrees of freedom of the movement can, in part or wholly, be measurableby the measurement system, at least in portions of the totality ofpossible relative positions.

FIG. 21 schematically shows an exploded view of an exemplary embodimentfor using a sensor system both for measuring the deflection of a probewhen probing a work piece and for determining the position and/oralignment of the probe or of a probe head during and/or after settingthe position and/or alignment. In the depicted exemplary embodiment, theprobe head (also referred to as measuring head), on which the probe isattached, is rotatable about a rotational axis. In other embodiments,other and/or additional degrees of freedom of the movement may exist forthe probe head and hence for the probe; i.e., the probe head can, inparticular, be moved in accordance with the degrees of freedom of themovement prior to probing a work piece by the probe. These degrees offreedom relate to movements of the probe head and hence of the proberelative to an arm of a coordinate measuring machine or relative toanother part of a coordinate measuring machine on which the probe headis arranged. This arm or part of the CMM can, in turn, be movable withrespect to a base of the CMM. By way of example, in the case of a CMMwith a portal design or gantry design, the probe head can be attached toa sleeve of the CMM and can be movable relative to the sleeve.

In the exemplary embodiment, which will now be described on the basis ofFIGS. 21 to 24, a probe head 130 is connected with rotational mobilityto a sleeve 142 (or with another in turn movable part) of a CMM by meansof e.g. a support plate 141 (or by means of a different attachment andsupport element). In particular, the support plate 141 can be affixed tothe sleeve 142 by means of passage bores 148 a, 148 b in the supportplate 141 and by means of bores 149 a, 149 b in the sleeve 142 and bymeans of attachment means (e.g. attachment screws) (not depicted in anymore detail). A drive motor 135 for generating a rotational movement ofthe probe head 130 about a rotational axis R is attached to the supportplate 141, for example by means of passage bores 138 a, 138 b in thesupport plate 141 and further attachment means (e.g. screws and nuts)(not described in any more detail). In the illustration of FIG. 21, therotational axis R extends in the horizontal direction. In particular,this direction can extend parallel to the X-axis of a Cartesiancoordinate system or coincide with this coordinate axis. By means of adrive shaft 136 of the drive motor 135, which, in the assembled state ofthe arrangement (e.g. FIG. 23), extends through a passage bore 137 inthe support plate 141, a rotational movement of a holder 138, whichholds the probe head 130, is generated when the drive motor 135 is inoperation. To this end, the free end region of the drive shaft 136 canbe connected in a rotationally secured manner to the holder 138. In thecase of a rotational movement of the drive shaft 136 about therotational axis R, the holder 138 and the probe head 130 held by theholder 138 are therefore rotated about the rotational axis R.

The drive motor 135 can be e.g. a stepper motor, which can be controlledin such a way that the probe head 130 can be brought into specific,predetermined rotational positions with respect to the rotational axis Rand relative to the support plate 141. In order to bring the probe head130 into these predetermined rotational positions, use may however alsobe made of a different drive. In particular, the rotational movement ofthe probe head can be performed manually. However, in this case, it ispreferable that the respective set rotational position can be secured byappropriate means (e.g. a clamping device) such that it remains in therotational position, even if external forces act, which forces aretransmitted to the rotation mechanism e.g. when probing a work piece 140by means of the probe 132 attached to the probe head 130.

FIG. 21 shows the probe 132 attached to the bottom of the probe head130, which probe is configured as a pin-shaped probe with a probingelement embodied as a probing sphere 133. However, use can also be madeof other probes. In particular, the probe 132 can be attached in areplaceable manner to the probe head 130. If the probe 132 or adifferent probe is attached to the probe head 130, the probe 132 can bedeflected from the neutral position shown in FIG. 21 using full lines,particularly when the work piece 140 is probed. The deflection isindicated by a small arrow pointing to the left, which is labeled withthe reference sign s. As a result of the deflection from the neutralposition, the probe performs a movement relative to the probe head 130.

Similar to as depicted in the principle sketch of FIG. 20, the probe isconnected to at least one sensor and/or one measuring body of ameasurement system. In the exemplary embodiment, five sensors s1 to s5are connected to a rod 134 of the probe head 130, wherein the rod 134 issecurely connected to the probe 132 such that, when the probe 132 isdeflected, the rod with the sensors is also deflected from a neutralposition. The position corresponding to the deflection of the probe 132is depicted by dashed lines. As a result of the secure connectionbetween rod 134 and probe 132, the position of the rod 134 deflected outof the neutral position is also depicted. However, the sensors s1 to s5attached to the rod 134 have not been depicted again for the deflectedposition for reasons of improved recognizability.

The sensors, together with the rod 134 and the probe head 130, are notonly moved in the case of a deflection of the probe 132 relative to thesupport plate 141, but also in the case of a rotational movement of theprobe head 130 driven by the drive motor 135 or in any other way.

As shown in FIG. 22 in particular, but as can also be identified fromFIG. 21, two sensors s2, s3; s4, s5 are in each case arranged at thesame distance from the rotational axis R or, expressed differently, arearranged at the same axial position in the longitudinal direction of therod 134. Furthermore, the sensors s1, s2; s3, s4 which are situated atthe same axial position are respectively configured to determine theposition of a different linear degree of freedom of the movement. Asshown, in particular, in the top view of FIG. 24 for the sensors s4, s5,the sensors are arranged offset from one another by 90° with respect tothe longitudinal axis of the rod 134. Furthermore, the assignedmeasuring bodies M of the sensors s4, s5 are also arranged angled by 90°with respect to one another. Here, the sensors s1 to s5 are situated ineach of the predetermined rotational positions in accordance with theexemplary embodiment between two magnets of a magnet pair and areconfigured to measure the magnetic field strength. Here, the magneticfield strength varies along an imaginary connecting line between themagnets of the magnetic field pair and it is therefore possible todetermine the position on the imagined connecting line between the twomagnets of the magnet pair using the magnetic field strength measured bythe sensor. Alternatively, the sensors and magnet pairs can beconfigured in such a way that the sensor measures a movementtransversely to the imagined connecting line of the magnets of themagnetic field pair. It is possible to identify for the two sensors s4and s5 shown in FIG. 24 that they are each carried by a sensor supportsT4, sT5 connected to the rod 134.

In FIGS. 21 to 24, the magnets, which, as measuring bodies, are assignedto the sensors, are respectively denoted by the capital letter M,followed by the number of the sensor (1 to 5) and in turn followed bythe number of the predetermined rotational position (1 to 3 in theexemplary embodiment). In the case of three rotational positions andfive sensors, fifteen pairs of magnets are therefore provided, as shownin FIG. 22. The position of the rod 134 shown in FIG. 22 is the firstpredetermined rotational position, which also corresponds to thepositions depicted in FIGS. 21, 23 and 24. In the second predeterminedrotational position, the longitudinal axis of the rod 134 would extendrotated by 45° about the rotational axis R in the clockwise direction inthe top view of FIG. 22. In the third predetermined rotational position,the longitudinal axis of the rod 134 would extend by 90° with respect tothe shown position about the rotational axis R in the clockwisedirection. Naturally, other variations of this embodiment are possible.By way of example, rotational positions can be predetermined at otherinclinations of the longitudinal axis of the rod. In the case of anappropriate arrangement or embodiment of the support plate or of adifferent support unit for carrying the measuring bodies, there couldalso be a distribution of the predetermined rotational positions over anangular range that is greater than 90°. It is also possible thatmeasuring bodies and sensors are interchanged for at least some of themeasuring body/sensor combinations. By way of example, the sensors couldbe attached to the support plate 141 and the measuring bodies (e.g. themagnet pairs) could be attached to the support rod 134.

In the exemplary embodiment of FIG. 21 to FIG. 24, the sensor s1 isconfigured to measure the exact position of the rod 134, and hence ofthe probe 132, in the direction of the longitudinal axis of the rod inthe predetermined rotational positions. As can be gathered from FIG. 24in particular, the fourth sensor s4 is able, in the predeterminedrotational positions, to measure the exact position of the rod 134 in adirection extending in a plane, which intersects the longitudinal axisof the rod 134. The sensor s5 is able, in the predetermined rotationalpositions, to measure the exact position with respect to a movementdirection, which likewise extends in the plane, which intersects thelongitudinal axis of the rod 134. Here, the plane, in particular,extends perpendicular to the longitudinal axis of the rod if smalldeviations from this ideal profile of the plane due to manufacturingtolerances and inexact reproduction of the predetermined rotationalposition are ignored. Such deviations can be taken into account, e.g.corrected, by calibration. However, precisely these deviations can bedetermined due to the measurement system with the measuring bodies M andthe sensors s1 to s5. In accordance with the arrangement of the sensorss4, s5 shown in FIG. 24, the sensors s2, s3 are able to determine theexact position of the rod 134 in respect of two further directionsextending parallel to the directions with respect to which the sensorss4, s5 determine the exact position of the rod. Here, the measuringdirections of the sensors s2, s3 are situated in a common plane, whichintersects the longitudinal axis of the rod 134 at a different axialposition of the rod and which extends parallel to the plane of themeasuring directions of the sensors s4, s5.

Overall, the sensors s1 to s5 are therefore able to determine the exactposition of the rod 134 and hence of the probe 132 in respect of fivedegrees of freedom of the movement. In the case of an appropriateembodiment of the arrangement and by calibration, it is possible toignore the remaining sixth degree of freedom of the movement (of theprobe 132 with respect to the sleeve 142) or the latter does not changeduring operation of the coordinate measuring machine. Hence, the samesensors (or alternatively, the same measuring bodies if the measuringbodies were to be attached to the rod 134) can determine the exactposition of the probe and hence, in particular, of the center of theprobing sphere 133 of the probe relative to the sleeve or relative toanother reference point, in any case with respect to specificpredetermined rotational positions of the probe head.

In the side view of FIG. 23, merely one of the sensors, namely sensors4, can be identified in order to keep the depiction simple. The probehead 130 with the probe 134 is situated in the first predeterminedrotational position, which is also shown in FIG. 22. Therefore, thesensor s4 is arranged between the magnets M4 a and M4 b. It is alsopossible to identify from the side view that the distance between themagnets M41 allows a rotational movement about the rotational axis Rinto another predetermined rotational position. To this end, FIG. 24shows two dashed lines extending from top to bottom in the plane of thefigure, which dashed lines mark the edges of the region in which asensor can be moved between the magnet pairs M41, M51. Furthermore, thedistance between the magnet pairs is selected to be so large that thesensors s1 to s5 do not impact on one of the magnets when the probe 132is deflected (as shown in FIG. 21).

FIG. 25 and FIG. 26 show a variant of the exemplary embodiment depictedin FIG. 21 to FIG. 24. The same reference signs denote the same orfunctionally equivalent elements. The exemplary embodiments have thefollowing differences: in one passage opening 147 of the support plate141, there is a bearing 145 which enables a rotational movement of thedrive shaft 136 of the drive motor 135, i.e. the drive shaft 136 ismounted with rotational mobility. Here, the bearing 145 is configured insuch a way that axial run-out and the radial run-out are negligiblysmall. By way of example, antifriction bearings (e.g. ball bearings orbearings containing cylindrical or spherical bearing elements) can bemanufactured and dimensioned in such a way that the radial run-out andthe axial run-out are negligibly small compared to the wobble error. Themeasurement arrangement shown in FIG. 25 and FIG. 26 therefore serves todetermine the wobble error. To this end, it is merely necessary tomeasure the distance of the rod 134 (or of a different part of the probehead 130) from the support plate 141 or from a different part securelyconnected to the sleeve 142. Here, this distance measurement in adirection extending approximately parallel to the rotational axis shouldbe performed with the greatest possible distance from the rotationalaxis R. In FIG. 25 and FIG. 26, a circle with an inclined arrow and afurther arrow extending in the distance measurement direction indicateschematically that provision is made for a corresponding distancesensor. By way of example, the distance sensor can be a capacitivesensor. However, other sensor types or measurement systems can also beused.

If a wobble movement now occurs during a rotational movement of theprobe head 130 (as indicated by dash—dotted lines extending obliquely tothe rotational axis R and crossing at a fixed point of the bearing 145),there is a change in the distance between the rod 134 and the supportplate 141. Corresponding distances, which can occur in the case of theindicated wobble movement, are denoted by U_(T1) and U_(T2). In the caseof the wobble movement, there is also a change in the position of theprobing sphere 133 of the stylus in a direction parallel to therotational axis R. FIG. 26 shows that a movement of the probing sphere133 in the same direction parallel to the rotational axis R can alsooccur when probing a work piece 150. In a circular, magnified region, itis possible to identify that the probing sphere 133 is no longer in theneutral position due to the presence of the work piece 150, but ratherhas been deflected by the magnitude s. This deflection can in turn bemeasured by the distance measurement between the rod 134 and the supportplate 141.

FIG. 25 and FIG. 26 moreover show that a reference point P can beselected e.g. at the lower end of the sleeve 142. It is indicated that aCartesian coordinate system X, Y, Z can be defined for this point P,wherein the X-axis extends parallel to the rotational axis R and whereinthe longitudinal axis of the rod 134 extends parallel to the Z-axis. Theprobe and the rod 134 of the probe head 130 connected thereto arerotatably mounted at a position L, at which the longitudinal axis of therod 134 intersects the rotational axis R, in order to enable thedeflection of the probe when probing the work piece 150. An axisextending perpendicular to the plane of the figure running through thisposition L extends parallel to the Y-direction of the Cartesiancoordinate system at the point P. The following will now discuss how themeasured distance between the support plate 141 and the rod 134 is usedto calculate the position of the probe and, in particular, the center ofthe probing sphere 133 of the probe. In the process, use is made of avector c_(A), which leads from the reference point P to the center ofthe rotational bearing 145, and a vector t_(A), which leads from thecenter of the rotational bearing 145 to the center of the probing sphere133. The following depiction of the correction using the distance valueu is however more general and also applies to other specific embodimentsthan the ones depicted in FIG. 25 and FIG. 26. The correction makes thefollowing assumptions:

The rotational axis has negligibly small axial and radial run-outs.

The rotational axis leads to significant wobble errors, which are to becorrected.

After a rotational movement, the rotational axis can be fixed in itsrotational position, e.g. clamped, or has a self-locking property due toits design (e.g. as a result of the drive motor).

As mentioned, the first two assumptions can be satisfied usingcommercially available precision antifriction bearings, which bear therotational movement. Furthermore, the assumption is made that therotational axis intersects the probe head at the point about which thestylus is mounted in a rotatable manner (bearing point L in FIG. 25 andFIG. 26). This bearing at the point L can, for example, be achieved by aspring parallelogram, as is the case in probe heads known per se.

The following illustration of the correction, like in the exemplaryembodiment in FIG. 25 and FIG. 26, only relates to one degree of freedomof the movement, which corresponds to the distance or to the position ina direction parallel to the rotational axis R and, under the madeassumptions, renders it possible to determine the wobble error. Takinginto consideration the Cartesian coordinate system at the referencepoint P, indicated in FIG. 25 and FIG. 26, the measurement systemsupplies a measured value in relation to the X-axis.

When probing a work piece (like the depicted probing of the work piece150 in the exemplary embodiment in accordance with FIG. 26), themeasured value u changes from when the work piece is touched by theprobing element of the probe, to be precise continuously with increasingdeflection of the probe from the neutral position thereof. It is knownthat a calibration for different deflections of the probe from theneutral position thereof renders it possible to establish a transmissionfunction or a transmission matrix, which, when probing a work piece tobe measured, renders it possible to calculate the coordinates of theprobed point on the work piece surface from the measured value u. In thefollowing text, the transmission function is denoted by f_(K)(u). In thegeneral case, not depicted here, it is possible that there are not onlypositions or measured values u in the X-direction, but that there arecorrespondingly also positions in the Y-direction and/or Z-direction ofthe Cartesian coordinate system of the reference point P, and it is alsopossible to establish a transmission function or transmission matrix forthis case by calibration. In a manner known per se, this function inparticular contains a correction due to the deformation of the probehead and of the components thereof, occurring when probing the workpiece.

In the following text, further consideration is given to the fact thatthe probe head is movable relative to the reference point P and,particularly in the exemplary embodiment of FIG. 25 and FIG. 26, hasrotational mobility about the rotational axis R. The calibration musttherefore result in appropriate corrections for all admissiblerotational positions of the probe head relative to the reference point(in particular of the sleeve). Therefore, a complete correction functionfor the position of the probing element of the probe is sought after:

p=P+t+f _(K)(u).

Here, P is the spatial vector of the reference point, which can be setto equal zero if the reference point lies at the origin of the observedcoordinate system, t denotes the vector leading from the reference pointP to the probing element, in particular to the center of the probingsphere 133, and f_(K)(u) is the aforementioned transmission function ortransmission matrix.

In the simplified case for the assumptions made above, a firstmeasurement signal u_(T1) (as e.g. depicted in FIG. 25) emerges after afirst rotational movement of the probe head about the rotational axis R.This measurement signal or the corresponding measured value, which isrelated to the X-axis, can be considered to be the neutral position ofthe calibration. In a manner known per se, it is now possible toestablish the parameters for the correction function and, at the sametime, the vector t without further rotational movement of the probehead. In order also to obtain a transmission function f_(K) for otherrotational positions of the probe head, it is possible, in the furtheradmissible rotational positions of the probe head, to use in each casethe difference between the measured value u measured there and thecorresponding measured value u_(T1) in the neutral position. Byrepeating the calibration for the further admissible rotationalpositions and by using the aforementioned difference between themeasured value u and the measured value u_(T1) in the neutral position,a further parameter of the calibration is available, which, under theassumptions made above, corresponds to the wobble error of therotational device. In this case, it is also not mandatory to perform anindependent calibration, e.g. by sensing a reference object, for eachpossible rotational position at which a work piece is subsequentlyintended to be sensed by the probe. If such a calibration is performedat a sufficient number of rotational positions, calibration values forother rotational positions can be obtained e.g. by interpolation.

Expediently, the vector t can be related to the wobble point, i.e. tothe point on the rotational axis R which does not change due to a wobblemovement. In the case of FIG. 25 and FIG. 26, this is the center of therotational bearing 145. In the equation specified above for thecorrection function p, the vector t can therefore be replaced by the sumof the vectors c_(A)+t_(A). Hence, the extended equation for thetransmission function or correction function p emerges:

p=P+c _(A) +t _(A) +f _(K)(u−u _(T1)).

The equation initially applies to merely a single rotational position.After a rotational movement into another rotational position of theprobe head, there is in general a different measured value u due to thewobble movement and hence a different neutral position U_(T2) for thedeflection of the probe when probing a work piece. It is now possible toonce again carry out a calibration process, i.e. the correction functionf_(K) can be established for the modified neutral position.

As described in the following, the wobble error can be taken intoaccount by its own associated correction component in the correctionfunction. Under the assumption that the wobble error only leads to smallangles of the longitudinal axis of the rod 134 with respect to theperpendicular to the rotational axis R, the rotational angle r_(y) ofthe rotational movement of the longitudinal axis of the rod 134 due tothe wobble movement can be calculated to a good approximation. Therotational angle r_(y) emerges from the equation

tan r _(y)=(u−u _(T))/d.

Here, u−u_(T) is the difference between the measured value and themeasured value for the neutral position. The wobble angle r_(y) can beused to determine a corresponding rotation matrix in equation (5)specified above. Here, d denotes the distance between the wobble pointand the bearing point L (see FIG. 25). The rotation matrix was labeledD_(A) above. Overall, the following correction function p thereforeemerges:

p=P+c _(A) +D _(A)(t _(A) +f _(K)(u−u _(T1))).

In other words, the rotation matrix D_(A) for correcting the wobbleerror acts on the sum of the vector t_(A) and of the calibrationfunction f_(K) in respect of a difference between the respectivemeasurement signal or measured value and the measured value from theneutral position in the first rotational position. In the case ofrelatively large wobble errors which lead to it no longer being possibleto consider the wobble angle r_(y) as being small, it is additionallypossible to take account of the corresponding displacement of thebearing point L in the equation.

A measurement system was described on the basis of FIGS. 21 to 24, whichcan in each case determine the exact position of the sensor support (therod 134 in the exemplary embodiment) for discrete predeterminedrotational positions. This concept can be transferred to otherapplications. By way of example, the sensors and/or measuring bodiesneed not be used both for exactly determining the support or the partsconnected thereto and for determining a deflection of a probe whenprobing a work piece. By way of example, this principle can also be usedin the other embodiments of a rotational device already mentioned aboveor in the aforementioned other uses of a rotational device. By way ofexample, a holder or support, which is rotatable due to a rotationaldevice, of a work piece (e.g. a rotary table) can have discrete,predetermined rotational positions and the exact rotational position,which can vary e.g. due to the load of the rotational device as a resultof the work piece or which can vary due to other influences, can bemeasured and corrected with the aid of the measurement system.

1. A configuration for at least one of measuring coordinates of aworkpiece or machining the workpiece, the configuration comprising: anarm of a coordinate measuring machine or of a machine tool, said armhaving a first part and a second part, said first part and said secondpart are regions of said arm which are situated at different axialpositions in a direction of a longitudinal axis of said arm and havemobility relative to each other due to at least one of mechanicalbending, thermal expansion or thermal contraction of said arm; anelongate element extending in the direction of the longitudinal axis ofsaid arm, said elongate element having a first axial end to which saidelongate element extends in the direction of the longitudinal axis ofsaid arm and having a second axial end, at which said elongate elementis connected to said first part and being situated opposite to saidfirst axial end with respect to the direction of the longitudinal axis,such that said first axial end moves relative to said second part whensaid first part and said second part move relative to each other; aplurality of sensors, each of said sensors being fixed to said elongateelement or to said second part; an evaluation device configured toevaluate measurement signals of said plurality of sensors; at least onemeasurement body fixed to said elongate element or to said second part,said measurement body being assigned said plurality of sensors, whereinin a case that said measurement body is fixed to said elongate element,said sensors are fixed to said second part, and wherein, in a case thatsaid measurement body is fixed to said second part, said sensors arefixed to said elongate element, such that each of said plurality ofsensors is capable of producing a measurement signal corresponding to aposition of said measurement body and thereby corresponding to arelative position of said first part and said second part; saidplurality of sensors and said measurement body configured such that saidplurality of sensors are capable of measuring the relative position ofsaid first part and said second part such that said evaluation devicedetermines the relative position of said first part and said second partand/or determines a relative orientation of said first part and saidsecond part, namely with respect to at least three degrees of freedom,the three degrees of freedom being a first and a second linear degree offreedom in two different directions extending perpendicularly to alongitudinal direction of said arm and a third linear degree of freedomin the longitudinal direction.
 2. The configuration according to claim1, wherein said plurality of sensors and said measurement body areconfigured such that said plurality of sensors are capable of measuringthe relative position of said first part and said second part such thatsaid evaluation device determines the relative position of said firstpart and said second part and/or determines the relative orientation ofsaid first part and said second part, namely with respect to at leastfive degrees of freedom, including the first, second and third lineardegrees of freedom, and a fourth and fifth rotational degree of freedomabout different directions extending perpendicularly to the longitudinaldirection.
 3. The configuration according to claim 1, wherein saidmeasurement body is one of a plurality of measurement bodies, a firstand a second of said plurality of measurement bodies are disposed withrespect to the longitudinal axis of said arm at a distance to eachother, wherein four of said plurality of sensors are configured todetermine a radial relative position of said first part and said secondpart, wherein said first of said plurality of measurement bodies isassigned to two of the four of said plurality of sensors and whereinsaid second of said plurality of measurement bodies is assigned toanother two of the four of said plurality of sensors.
 4. Theconfiguration according to claim 3, wherein said first and said secondof said plurality of measurement bodies are formed at said elongateelement.
 5. The configuration according to claim 1, wherein saidelongate element extends in an interior space of said arm.
 6. Theconfiguration according to claim 1, wherein said second part has aninterface for fixing and attaching a sensor head, a rotational device, asensor device having an integrated rotational device or a touch probe.7. The configuration according to claim 1, further comprising a dampingdevice for damping mechanical vibrations of said elongate element. 8.The configuration according to claim 1, wherein: said at least onemeasurement body is one of a plurality of measurement bodies, each ofsaid plurality of measurement bodies is fixed to said elongate elementor to said second part, an assigned measurement body being one of saidplurality of measurement bodies assigned at least one sensor of saidplurality of sensors, wherein in a case that said assigned measurementbody is fixed to said elongate element, said at least one sensor isfixed to said second part, and wherein, in a case that said assignedmeasurement body is fixed to said second part, said at least one sensoris fixed to said elongate element, such that each of said plurality ofsensors is capable of producing a measurement signal corresponding to aposition of said measurement bodies and thereby corresponding to therelative position of said first part and said second part; and saidplurality of sensors and said measurement bodies are configured suchthat said plurality of sensors are capable of measuring the relativeposition of said first part and said second part such that saidevaluation device determines the relative position of said first partand said second part and/or determines the relative orientation of saidfirst part and said second part, namely with respect to the at leastthree degrees of freedom.
 9. A method of manufacturing a configurationfor at least one of measuring coordinates of a workpiece or machiningthe workpiece, the method comprises: providing an arm of a coordinatemeasuring machine or of a machine tool, the arm having a first part anda second part, the first part and the second part are regions of the armand are situated at different axial positions in a direction of alongitudinal axis of the arm and which have mobility relative to eachother due to at least one of mechanical bending, thermal expansion orthermal contraction of the arm; providing an elongate element extendingin the direction of the longitudinal axis of the arm, the elongateelement having a first axial end to which the elongate element extendsin the direction of the longitudinal axis of the arm and having a secondaxial end, at which the elongate element is connected to the first partand which is situated opposite to the first axial end with respect tothe direction of the longitudinal axis, such that the first axial endmoves relative to the second part when the first part and the secondpart move relative to each other; providing a plurality of sensors, andfixing each of the sensors to the elongate element or to the secondpart; providing an evaluation device configured to evaluate measurementsignals of the plurality of sensors; providing at least one measurementbody and fixing the measurement body to the elongate element or to thesecond part, the measurement body being assigned to the plurality ofsensors, wherein, in case that the measurement body is fixed to theelongate element, the sensors are fixed to the second part, and wherein,in a case that the measurement body is fixed to the second part, thesensors are fixed to the elongate element, such that each of theplurality of sensors is capable of producing a measurement signalcorresponding to a position of the measurement body and therebycorresponding to a relative position of the first part and the secondpart; and configuring the plurality of sensors and the measurement bodysuch that the plurality of sensors are capable of measuring the relativeposition of the first part and the second part such that the evaluationdevice determines the relative position of the first part and the secondpart and/or determines a relative orientation of the first part and thesecond part, namely with respect to at least three degrees of freedom,the three degrees of freedom being a first and a second linear degree offreedom in two different directions extending perpendicularly to alongitudinal direction of the arm and a third linear degree of freedomin the longitudinal direction.
 10. The method according to claim 9,which further comprises configuring the plurality of sensors and themeasurement body such that the plurality of sensors are capable ofmeasuring the relative position of the first part and the second partsuch that the evaluation device determines the relative position of thefirst part and the second part and/or determines the relativeorientation of the first part and the second part, namely with respectto at least five degrees of freedom, including the first, second andthird linear degree of freedom, and a fourth and fifth rotational degreeof freedom about different directions extending perpendicularly to thelongitudinal direction.
 11. The method according to claim 9, wherein themeasurement body is one of a plurality of measurement bodies, a firstand a second of the plurality of measurement bodies are disposed withrespect to the longitudinal axis at a distance to each other, whereinfour of the plurality of sensors are configured to determine a radialrelative position of the first part and the second part, wherein thefirst of the plurality of measurement bodies is assigned to two of thefour of the plurality of sensors and wherein the second of the pluralityof measurement bodies is assigned to another two of the four of theplurality of sensors.
 12. The method according to claim 11, whichfurther comprises forming the first and the second of the plurality ofmeasurement bodies at the elongate element.
 13. The method according toclaim 9, which further comprises disposing the elongate element so thatthe elongate element extends in an interior space of the arm.
 14. Themethod according to claim 9, which further comprises configuring thesecond part to comprise an interface for fixing and attaching a sensorhead, a rotational device, a sensor device having an integratedrotational device or a touch probe.
 15. The method according to claim 9,which further comprises providing a damping device for dampingmechanical vibrations of the elongate element.
 16. The method accordingto claim 9, which further comprises: forming the at least onemeasurement body as one of a plurality of measurement bodies, each ofthe plurality of measurement bodies is fixed to the elongate element orto the second part, an assigned measurement body being one of theplurality of measurement bodies assigned at least one sensor of theplurality of sensors, wherein in the case that the assigned measurementbody is fixed to the elongate element, the at least one sensor is fixedto the second part, and wherein, in the case that the assignedmeasurement body is fixed to the second part, the at least one sensor isfixed to the elongate element, such that each of the plurality ofsensors is capable of producing a measurement signal corresponding to aposition of said measurement bodies and thereby corresponding to therelative position of said first part and said second part; and theplurality of sensors and the measurement bodies are configured such thatthe plurality of sensors are capable of measuring the relative positionof the first part and the second part such that the evaluation devicedetermines the relative position of the first part and the second partand/or determines the relative orientation of the first part and thesecond part, namely with respect to the at least three degrees offreedom.
 17. A method of operating a configuration for at least one ofmeasuring coordinates of a workpiece or machining the workpiece, whichcomprises the steps of: using an arm of a coordinate measuring machineor of a machine tool, the arm having a first part and a second part, thefirst part and the second part being regions of the arm which aresituated at different axial positions in a direction of a longitudinalaxis of the arm and which have mobility relative to each other due to atleast one of mechanical bending, thermal expansion or thermalcontraction of the arm; using an elongate element extending in thedirection of the longitudinal axis of the arm, the elongate elementhaving a first axial end to which the elongate element extends in thedirection of the longitudinal axis of the arm and having a second axialend, at which the elongate element is connected to the first part andwhich is situated opposite to the first axial end with respect to thedirection of the longitudinal axis, such that the first axial end movesrelative to the second part when the first part and the second part moverelative to each other; using a plurality of sensors, each of thesensors being fixed to the elongate element or to the second part; usingan evaluation device for evaluating measurement signals of the pluralityof sensors; using at least one measurement body, being fixed to theelongate element or to the second part, the measurement body beingassigned to the plurality of sensors, wherein in case that themeasurement body is fixed to the elongate element, the sensors are usedwhile being fixed to the second part, and wherein in case that themeasurement body is fixed to the second part, the sensors are used whilebeing fixed to the elongate element, such that each of the plurality ofsensors produces a measurement signal corresponding to a position of themeasurement body and thereby corresponding to a relative position of thefirst part and the second part; and using the plurality of sensors andthe measurement body such that the plurality of sensors measure therelative position of the first part and the second part such that theevaluation device determines at least one of the relative position ofthe first part and the second part or a relative orientation of thefirst part and the second part, namely with respect to at least threedegrees of freedom, the three degrees of freedom being a first and asecond linear degree of freedom in two different directions extendingperpendicularly to a longitudinal direction of the arm and a thirdlinear degree of freedom in the longitudinal direction.
 18. The methodaccording to claim 17, which further comprises using the plurality ofsensors and the measurement body such that the plurality of sensorsmeasure the relative position of the first part and the second part suchthat the evaluation device determines at least one of the relativeposition of the first part and the second part or the relativeorientation of the first part and the second part, namely with respectto at least five degrees of freedom, including the first, second andthird linear degrees of freedom, and a fourth and fifth rotationaldegrees of freedom about different directions extending perpendicularlyto the longitudinal direction.
 19. The method according to claim 17,wherein the measurement body is one of a plurality of measurement bodiesand a first and a second of the plurality of measurement bodies are usedwhile being disposed with respect to the longitudinal axis at a distanceto each other, wherein four of the plurality of sensors determine aradial relative position of the first part and the second part, whereinthe first of the plurality of measurement bodies is assigned to two ofthe four of the plurality of sensors and wherein the second of theplurality of measurement bodies is assigned to another two of the fourof the plurality of sensors.
 20. The method according to claim 19, whichfurther comprises forming the first and the second of the plurality ofmeasurement bodies at the elongate element.
 21. The method according toclaim 17, which further comprises using the elongate element while beingdisposed so that the elongate element extends in an interior space ofthe arm.
 22. The method according to claim 17, which further comprisesusing the second part as an interface for fixing and attaching a sensorhead, a rotational device, a sensor device having an integratedrotational device or a touch probe.
 23. The method according to claim17, which further comprises damping mechanical vibrations of theelongate element by using a damping device.